Revisiting Waves

Q.

The speed of transverse waves in a string depends on:

1. Shear modulus and linear mass density

2. tension in it and its linear mass density

3. Pressure on the string

4. Young's modulus and linear mass density

Q.

The equation of a simple harmonic progressive wave is given by
y = 8sin (0.628x – 12.56t)
where x and y are in cm and t is in second.
Find the phase difference in degrees between two particles at a distance of 2.0cm apart at any instant.

1. 72

2. 64

3. 57

4. 45

Q. A microphone of cross-sectional area 0.80 $c{m}^2$ is placed in front of a small speaker emitting 3.0 W of sound output. If the distance between the microphone and the speaker is 2.0 m, how much energy falls on the microphone in 5.0 s?

1. $12\mu J$

2. $80\mu J$

3. $24\mu J$

4. $30\mu J$

Q. A steel wire of length 64 cm weighs 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it?

Q.

Ultrasonic waves of frequency 4.5 MHz are used to detect tumor in soft tissues. The speed of sound in tissue is 1.5 km s${}^{-1}$ and that in air is 340 m s${}^{-1}$. Find the wavelength of this ultrasonic wave in tissue.

1. 333 m

2. 3.33 $\times$ 10${}^{-4}$ m

3. 1000 m

4. 10-4 m

Q. A source of sound of frequency $50H_Z$ is producing longitudinal waves in air. The amplitude of vibrations of air particles is 5mm and the speed of the wave is $330m{s}^{-1}$. Write the equation of the wave.

1. $y=5\times {10}^{-3}sin[100\pi t-\frac{100\pi x}{33}]$
2. $y=0.05sin[220\pi t-\frac{\pi x}{3}]$
3. $y=0.05sin[110\pi t-\frac{2\pi x}{3}]$
4. $y=0.05sin[110\pi t-\frac{\pi x}{3}]$

Q.

A wave of wavelength 0.60 cm is produced in air and it travels at a speed of 300 m s${}^{-1}$. Will it be audible?

1. Yes

2. No

3. Data insufficient

Q.

A body is vibrating 6000 times in a minute. If the velocity of sound is 360 m/s. Find

(i) the frequency in (Hz) (ii) Wavelength of sound

1. 100 Hz, 3.6 m
2. 600 Hz, 3.6 m
3. 60 Hz, 6 m
4. 6000 Hz, 0.06 m

Q. Consider a pulse created on the horizontal string highlighted. The net force applied by particles $A$ and $C$ on $B$ will be in

1. upward direction
2. downward direction
3. left direction
4. right direction

Q. 247.A 5.5m length string has a mass of 0.35kg.If the tension in the string is 77N.The speed of a transverse wave on the string is

Q. A source of sound of frequency $50H_Z$ is producing longitudinal waves in air. The amplitude of vibrations of air particles is 5mm and the speed of the wave is $330m{s}^{-1}$. Write the equation of the wave.

1. $y=5\times {10}^{-3}sin[100\pi t-\frac{100\pi x}{33}]$
2. $y=0.05sin[220\pi t-\frac{\pi x}{3}]$
3. $y=0.05sin[110\pi t-\frac{2\pi x}{3}]$
4. $y=0.05sin[110\pi t-\frac{\pi x}{3}]$

Q.

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given

$y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right]$

i. What is the frequency of vibration?

ii. What are the positions of the nodes?

iii. What is the length of the string?

iv. What is the wavelength and the speed of two travelling waves that can interfere to give this vibration?

1. $300Hz,0,10cm,20cm,30cm,L=30cm,\lambda =20cm,v=60m{s}^{-1}$

2. $600Hz,0,15cm,30cm,L=30cm,\lambda =20cm,v=60m{s}^{-1}$

3. $300Hz,0,10cm,20cm,L=20cm,\lambda =20cm,v=60m{s}^{-1}$

4. None of these

Q. The sound from a very high burst of fireworks takes 5 s to arrive at the observer. The burst occurs 1662 m above the observer and travels vertically through two stratifier layers of air, the top one of thickness
$d_1$ at $0^{\circ }C$ and the bottom one of thickness $d_2$ at ${20}^{\circ }C$. Then (assume velocity of sound at $0^{\circ }C$ is 330 m/s)

1. $d_1=342m$
2. $d_2=1320m$
3. $d_1=1485m$
4. $d_2=342m$