Transmission of Wave

Q.

What is path difference formula?

Q.

What is the difference between TE and TM mode?

Q.

If the speed of a wave doubles as it passes from shallow water into deeper water, its wavelength will be:

1. Unchanged

2. Doubled

3. Quadrupled

4. Halved

Q.

If the speed of a transverse wave on a stretched string of length $1m$ is $60m{s}^{-1}$, what is the fundamental frequency of vibration?

Q.

A wave of frequency $500Hz$ has a velocity of ${360}^{°}m{s}^{-1}.$ Calculate the distance between two points that are ${60}^{°}$ out of phase

1. $12cm$

2. $18cm$

3. $17cm$

4. $25cm$

Q. A composite string is made by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. A transverse wave pulse. $y=\left(6\text{mm}\right)\sin (5t+40x)$, where '$t$' is in seconds and '$x$' is in meters, is sent along the lighter string towards the joint. The joint is at $x=0$. The equation of the wave pulse reflected from the joint is $y=\left(2\text{mm}\right)\sin (5t-40x+\pi )$. The percentage of the power transmitted to the heavier string through the joint is approximately

1. $33\%$
2. $89\%$
3. $67\%$
4. $75\%$

Q. A pulse travelling on string fixed at one end and free at other end as shown figure. Choose the correct option.

1. Point A represents node
2. Point B represents antinode
3. Point B represents node
4. Both (a) and (b)

Q. Which quantity will always remain same when an incident wave transmits from one medium to other?

1. Wave speed
2. Amplitude
3. Wavelength
4. Frequency

Q. A pulse (shown here) is reflected from the rigid wall $A$ and then from free end $B$. The shape of the string after these $2$ reflections will be -

1. 
2. 
3. 
4. 

Q. The figure shows at time $t=0\text{sec}$, a rectangular and triangular pulse on a uniform wire. They are approaching each other. The pulse speeds are $0.5\text{cm/s}$ each. The resultant pulse at $t=2\text{sec}$ is

1. 
2. 
3. 
4. 

Q. Two strings are attached to each other as shown in the figure. The linear mass density of the second string is four times that of the first string and the boundary between the two strings is at $x=0$. The wave equation of the incident wave at the boundary is $y_i=A_i\cos (k_{1}x-{\omega }_{1}t)$. Then, which of the following correctly represents the equation of the transmitted wave? Assume, tension in the two strings are same.

1. $y_t=\frac{3}{2}{A}_i\cos (k_{1}x-{\omega }_{1}t)$
2. $y_t=\frac{2}{3}{A}_i\cos (k_{1}x-{\omega }_{1}t)$
3. $y_t=\frac{3}{2}{A}_i\cos (2k_{1}x-{\omega }_{1}t)$
4. $y_t=\frac{2}{3}{A}_i\cos (2k_{1}x-{\omega }_{1}t)$

Q. A pulse (shown here) is first reflected from the free end $A$ and then from the rigid end $B$. The phase difference between initial incident pulse and final reflected pulse after two reflections is

1. $\pi$
2. $2\pi$
3. $0$
4. $3\pi$

Q. Two strings $1$ and $2$ make a junction of partly reflected and partly transmitted waves. The linear mass density of string $2$ is four times that of string $1$, and the boundary between the two strings is at $x=0$. The expression for the incident wave is $y_i=A_i\cos (k_{1}x-{\omega }_{1}t)$. Which of the following relations is correct, if average power carried by the incident wave, transmitted wave and reflected wave are $P_i,P_t\&P_r$ respectively? [Assume tension in string $1$ and $2$ to be the same]

1. $P_i=P_t-P_r$
2. $P_i=\frac{P_i}{P_r}$
3. $P_i=P_t\times P_r$
4. $P_i=P_t+P_r$

Q. Figure shows an incident pulse $P$ reflected from a rigid support. Which one of the following options represent the reflected pulse?

1. 
2. 
3. 
4. 

Q. Two strings $A$ and $B$ made of same material are stretched by same tension. The radius of cross-section of string $A$ is double the radius of cross-section of string $B$. A transverse wave travels through string $A$ with speed $v_A$ and through string $B$ with speed $v_B$. The ratio $\frac{v_A}{v_B}$ is

1. $\frac{1}{2}$
2. $2$
3. $\frac{1}{4}$
4. $4$

Q. The speed of a transverse wave travelling through a wire having a length $50\text{cm}$and mass $5.0\text{g}$ is $80\text{m/s}$. The area of cross-section of the wire is $1.0{\text{mm}}^2$ and its Young's modulus is $16\times {10}^{11}{\text{N/m}}^2$. Find the extension in the wire with respect to its natural length.

1. $0.01\text{mm}$
2. $0.3\text{mm}$
3. $0.02\text{mm}$
4. $0.04\text{mm}$

Q. If a wave is going from one medium to another, then

1. its frequency changes
2. its wavelength does not change
3. its speed does not change
4. its amplitude may change

Q. A string of length $7\text{m}$ has a mass of $0.035\text{kg}$. If the tension in the string is $60.5\text{N}$, then speed of a wave on the string is:

1. $77\text{m/s}$
2. $102\text{m/s}$
3. $110\text{m/s}$
4. $165\text{m/s}$

Q. A composite string is made up by joining two strings of different mass per unit length $\mu$ and $4\mu$. The composite string is under the same tension. A transverse wave pulse is sent along the lighter string towards the joint. The ratio of wave number of incident wave to the transmitted wave is

1. $2:1$
2. $1:2$
3. $3:2$
4. $2:3$

Q. Equation of a plane progressive wave is given by $y=0.5\text{sin}3\pi (t-\frac{x}{3})$. On reflection from a denser medium its amplitude becomes $\frac{2}{5}$ of the amplitude of the incident wave. The equation of the reflected wave is

1. $0.2\text{sin}\left(\pi \right(3t+x\left)\right)$
2. $-0.2\text{sin}(3\pi t+\pi x)$
3. $0.5\text{sin}(\pi t+x)$
4. $0.2\text{sin}\left(\pi \right(3t-x\left)\right)$

Q. A harmonic wave is travelling on string $1$. At the junction with string $2$, it is partly reflected and partly transmitted. The linear mass density of string $2$ is $9$ times that of string $1$, and that the boundary between the two strings is at $x=0$. If the expression for the incident wave is
$y_i=\left(3\text{cm}\right)\cos \left[\right(3.14{\text{cm}}^{-1})x-(314{\text{rad s}}^{-1}\left)t\right]$. What is the expression for the transmitted waves?

1. $y_t=\left(3\text{cm}\right)\cos \left[\right(3.14{\text{cm}}^{-1})x-(314{\text{rad s}}^{-1}\left)t\right)]$
2. $y_t=\left(1.5\text{cm}\right)\cos \left[\right(3{\text{cm}}^{-1})x-(9.42{\text{rad s}}^{-1}\left)t\right]$
3. $y_t=\left(3\text{cm}\right)\cos \left[\right(9.42{\text{cm}}^{-1})x-(3.14{\text{rad s}}^{-1}\left)t\right]$
4. $y_t=\left(1.5\text{cm}\right)\cos \left[\right(9.42{\text{cm}}^{-1})x-(314{\text{rad s}}^{-1}\left)t\right]$

Q.

The harmonic wave $y_i=(2.0\times {10}^{-3})cos\pi (2.0x-50t)$ travels along a string toward a boundary at $x=0$ with a second string. The wave speed on the second string is $50m/s$. What are the expressions for reflected and transmitted waves. Assume SI units

1. $6.67\times {10}^{-4}cos\pi (2.0x+50t),2.67\times {10}^{-3}cos\pi (x-50t)$

2. $6.67\times {10}^{-4}cos\pi (2.0x-50t),2.67\times {10}^{-3}cos\pi (x-50t)$

3. $6.67\times {10}^{-4}cos\pi (2.0x+50t+\pi ),2.67\times {10}^{-3}cos\pi (x-50t)$

4. $6.67\times {10}^{-4}cos\pi (2.0x-50t+\pi ),2.67\times {10}^{-3}cos\pi (x-50t)$

Q. Figure shows a string of linear mass density $1.0\text{g/cm}$ on which a wave pulse is travelling.


Find the time taken by the pulse in travelling through a distance of $50\text{cm}$ on the string. Take $g=10{\text{m/s}}^2$

1. $0.04\text{s}$
2. $0.03\text{s}$
3. $0.05\text{s}$
4. $0.08\text{s}$

Q.

The wavelength of waves produced on the surface of the water is 20 cm. If the wave velocity is 24 m/s calculate the number of waves produced in one second.

Q. The T.V transmission tower in Delhi has a height of $240\text{m}$. The distance up to which the broadcast can be received (taking the radius of earth to be $6.4\times {10}^{6}m)$ is (in km) (round off to nearest integer)

Q. A wave travelling on a string is transmitted to other string of different density, gets partially reflected at the junction. The reflected wave is inverted in shape as compared to the incident wave. If the incident wave has wavelength ${\lambda }_1$ and the transmitted wave ${\lambda }_2,$ then

1. ${\lambda }_2>{\lambda }_1$
2. ${\lambda }_2={\lambda }_1$
3. ${\lambda }_2<{\lambda }_1$
4. Cannot be predicted

Q. Two strings are attached to each other as shown in the figure. The linear mass density of the second string is $16$ times that of the first string and the boundary between the two strings is at $x=0$. The incident wave is given by $y=0.01\cos (20x-100t)$. Then, the ratio of amplitude of reflected wave to amplitude of transmitted wave is:
[Assume, tension in both the strings is same]

1. $2:3$
2. $3:2$
3. $5:9$
4. $9:5$

Q. The pulse shown is figure has a speed $8\text{cm/s}$. The linear mass density of right string is 4 times that of the left string. What is ratio of the heights of the transmitted pulse and the reflected pulse?
[Assume tension to be same]

1. 4
2. 1
3. 2
4. 6

Q. A pulse is travelling on a stretched string fixed at one end with velocity $2\text{cm/s}$ as shown in the figure. At $t=0\text{s}$, center of pulse is $4\text{cm}$ apart from the fixed end. The shape of string at $t=2\text{s}$ is

1. 
2. 
3. 
4. 

Q. A sinusoidal wave represented as $y_i=0.004\cos \pi (4x-100t)\text{m}$ travels along a string towards a boundary at $x=0$ with a second string. If the wave speed on the second string is $50\text{m/s}$ , then which of the following statement(s) is/are correct?

1. Amplitude of the reflected wave is $\frac{4}{3}\times {10}^{-3}\text{m}$.
2. Amplitude of the transmitted wave is $\frac{16}{3}\times {10}^{-3}\text{m}$.
3. Amplitude of the reflected wave is $\frac{16}{3}\times {10}^{-3}\text{m}$.
4. Amplitude of the transmitted wave is $\frac{4}{3}\times {10}^{-3}\text{m}$.