SHM

Q. At $t=0$, a transverse wave pulse travelling in the positive $x$ direction with a speed of $2\text{m/s}$ in a long wire is described by the function, $y=\frac{6}{x^2},$ given that $x\ne 0$. Transverse velocity of a particle at $2\text{m}$ and at $2\text{s}$ will be

1. $3\text{m/s}$ upwards
2. $3\text{m/s}$ downwards
3. $8\text{m/s}$ upwards
4. $8\text{m/s}$ downwards

Q. A point mass oscillates along the $x-$axis according to the law $x=x_0\cos (\omega t-\pi /4)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then

1. $A=x_0,\delta =-\pi /4$
2. $A=x_0{\omega }^2,\delta =\pi /4$
3. $A=x_0{\omega }^2,\delta =3\pi /4$
4. $A=x_0{\omega }^2,\delta =-\pi /4$

Q. A plane progressive wave is represented by the equation $Y=0.1sin(200\pi t-\frac{20\pi x}{17})$ where y is displacement in m, t in second and x is distance from a fixed origin in meter. The frequency, wavelength and speed of the wave respectively are

1. 100 Hz, 1.7 m, 170 m/s
2. 80 Hz, 1.1 m, 90 m/s
3. 120 Hz, 1.25 m, 207 m/s
4. 150 Hz, 2.4 m, 200 m/s

Q. Which of the following is not true for this progressive wave $y=4sin2\pi (\frac{t}{0.02}-\frac{x}{100})$ where y and x are in cm & t in sec

1. Its amplitude is 4 cm
2. Its frequency is 50 cycles/sec
3. Its propagation velocity is 50 x 10³ cm/sec
4. Its wavelength is 100 cm

Q. The equation of progressive wave in a wire is given by $y=0.15sin\left[2\pi (15t-\frac{x}{10})\right]$
Where the distance is in meters and time in seconds.
Determine i) amplitude, ii) frequency, iii) wavelength and iv) velocity of the wave

1. $A=0.1m,f=15Hz,v=15m/s,\lambda =1m$
2. $A=0.15m,f=150Hz,v=150m/s,\lambda =1m$
3. $A=0.15m,f=15Hz,v=150m/s,\lambda =10m$
4. $A=0.15m,f=30Hz,v=15m/s,\lambda =10m$

Q. The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m, 333 m/s, and 110 Hz. Write the equation of the wave.

1. $y=0.05sin110(t-\frac{x}{333})$
2. $y=0.05sin110\pi (t-\frac{x}{333})$
3. $y=0.05sin220(t-\frac{x}{333})$
4. $y=0.05sin220\pi (t-\frac{x}{333})$

Q. The string of a musical instrument is $90cm$ long and has a fundamental frequency of $124Hz$. The distance $x$ from one end of the string where it should be pressed to produce a fundamental frequency of $186Hz$

1. $50cm$
2. $45cm$
3. $75cm$
4. $60cm$

Q. $y(x,t)=0.8/\left[\right(4x+5t{)}^2+5]$ represents a moving pulse, where $x$ and $y$ are in metres and $t$ is in seconds, then

1. pulse is moving in $+x$ direction
2. in $2\text{s}$ it will travel a distance of $2.5\text{m}$
3. its maximum displacement along y-axis is $0.16\text{m}$
4. it is a symmetric pulse

Q. Beats are produced by two waves $y_1=asin200\pi t$ and $y_2=asin208\pi t$. The number of beats heard per second is

1. 1
2. 0
3. 4
4. 8

Q. A transverse wave is represented by:

1. 40 cm
2. 20 cm
3. 10 cm
4. 60 cm

Q. A string of length $1\text{m}$ and mass $5\text{g}$ is fixed at both ends. The tension in the string is $8.0\text{N}$. The string is set into vibration using an external vibrator of frequency $100\text{Hz}$. The separation between successive nodes on the string is close to:

1. $10.0\text{cm}$
2. $33.3\text{cm}$
3. $16.6\text{cm}$
4. $20.0\text{cm}$

Q.

The given figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?

1. $1.0m{s}^{-1}$

2. $1.5m{s}^{-1}$

3. $2.0m{s}^{-1}$

4. $2.5m{s}^{-1}$

Q. The transverse wave propagating through a medium is given by $y=A\cos 2\pi [ft-\frac{x}{\lambda }]$. If maximum particle velocity of medium is two times the velocity of wave through medium, then.

1. $\lambda =3.14A$
2. $\lambda =6.28A$
3. $6.28\lambda =A$
4. $3.14\lambda =A$

Q. A transverse wave is described by the equation $y=y_{0}sin2\pi$($ft-\frac{\pi }{\lambda }$). The maximum particle velocity is equal to four times the wave velocity if :

1. $\lambda$ = $\frac{\pi y_0}{4}$
2. $\lambda$ = $\frac{\pi y_0}{2}$
3. $\lambda$ = $2\pi y_0$
4. $\lambda$ = $\pi y_0$

Q. Two second sources produce progressive waves given by $y_1=12\cos 100\pi t$ and $y_2=4\cos 102\pi t$ neat the ear of an observer. When sounded together, the observer will hear.

1. $2$ beats per two sound source with an intensity ratio of maximum to minimum nearly $4:1$
2. $1$ beat per second with an intensity ratio of maximum to minimum nearly $\sqrt{2}:1$
3. $1$ beats per second with an intensity ratio of maximum to minimum nearly $9:1$
4. $1$ beat per second with an intensity ratio of maximum to minimum nearly $4:1$

Q. A progressive wave of frequency $500Hz$ is travelling with a velocity $360m{s}^{-1}$. How far are two points ${60}^{\circ }$ out of phase?

1. $0.12m$
2. $0.18m$
3. $0.06m$
4. $0.24m$

Q. A point mass oscillates along the $x-$axis according to the law $x=x_0\cos (\omega t-\pi /4)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then

1. $A=x_0,\delta =-\pi /4$
2. $A=x_0{\omega }^2,\delta =\pi /4$
3. $A=x_0{\omega }^2,\delta =-\pi /4$
4. $A=x_0{\omega }^2,\delta =3\pi /4$

Q. Standing waves are setup in a string of length 240 cm clamped horizontally at both ends. The separation between any two consecutive points were displacement amplitude is $3\sqrt{2}$ cm is 20 cm. The standing waves were setup by two travelling waves of equal amplitude of 3 cm. The overtone in which the string is vibrating will be :

1. 5th
2. 2nd
3. 3rd
4. 4th

Q. If the slope is $s$, wave velocity is $v_w$ and particle velocity of $v_p$ then

1. $v_p=s{v}_w$
2. $v_p=\frac{-v_w}{s}$
3. $v_p=-s{v}_w$
4. $v_p=\frac{v_w}{s}$

Q. A transverse sinusoidal wave moves along a string in the positive $x-$direction at a speed of $10\text{cm/s}$. The wavelength of the wave is $0.5m$ and its amplitude is $10cm$. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $0.05m$ is

1. $\frac{\sqrt{3}\pi }{50}\hat{j}\text{m/s}$
2. $-\frac{\sqrt{3}\pi }{50}\hat{j}\text{m/s}$
3. $\frac{\sqrt{3}\pi }{50}\hat{i}\text{m/s}$
4. $-\frac{\sqrt{3}\pi }{50}\hat{i}\text{m/s}$

Q. (b) If the pipe is filled with air at pressure $1.00\times {10}^5$ Pa and density $1.20kg/m^3$, what will be the amplitude A and wavelength $\lambda$ of a longitudinal wave with intensity $3.00\times {10}^{-6}W/m^2$ and frequency 3400 Hz?

Q. A point mass oscillates along the $x-$axis according to the law $x=x_0\cos (\omega t-\pi /4)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then

1. $A=x_0,\delta =-\pi /4$
2. $A=x_0{\omega }^2,\delta =\pi /4$
3. $A=x_0{\omega }^2,\delta =-\pi /4$
4. $A=x_0{\omega }^2,\delta =3\pi /4$

Q. In brass, the velocity of longitudinal waves is $100times$ the velocity of transverse waves. If $Y=1\times {10}^{11}N/m^2,$ then the stress in the wire is

1. ${10}^7/N/m^2$
2. ${10}^8/N/m^2$
3. ${10}^9/N/m^2$
4. ${10}^{10}/N/m^2$

Q. Two waves $y_1=8\sin (2x-3t)$ and $y_2=6\sin (2x-3t-\frac{\pi }{2})$ are superimposed. Then, which of the following is/are correct.
$(y_1$ and $y_2$ are in $\text{cm})$

1. Phase difference between $y_1$ and $y_2$ is $\frac{\pi }{2}$.
2. Velocity of $y_1$ and $y_2$ is $1.5{\text{cm s}}^{-1}$
3. Amplitude of resultant wave is $20\text{cm}$.
4. Amplitude of resultant wave is $12\text{cm}$.

Q. The equation of a light wave is written as $y=Asin(kx-\omega t)$. Here, y represents:

1. displacement of either particles
2. density of the medium
3. Pressure in the medium
4. electric field

Q. Oscillation of a $600Hz$ tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is $400m/s.$ The standing wave has four loops and an amplitude of $2.0mm$. What is the length of the string?

Q. A plane progressive wave is given by $y=25\cos (2\pi t-\pi x)$ Then the amplitude and frequency are respectively

1. 25, 100
2. 25, 1
3. 25, 2
4. $50\pi ,2$

Q. Three consecutive resonant frequencies of string are $90,150$ and $210Hz.$ If the length of the string is $80cm$ what is the speed of the transverse wave in the string ?

1. $45m/s$
2. $48m/s$
3. $80m/s$
4. $96m/s$

Q. The average value of the wave-form shown in the figure above is

1. $15\sqrt{2}$
2. $10\sqrt{2}$
3. $10$
4. $15$

Q. Two strings $A$ and $B$, made of same material, are stretched by same tension. The radius of string $A$ is double of the radius of $B$. A transverse wave travels on $A$ with speed $v_A$ and on $B$ with speed $v_B$. The ratio $v_A/v_B$ is

1. $2$
2. $1/2$
3. $1/4$
4. $4$