An observer is approaching a stationary source with a velocity $\frac{1}{4}$th of the velocity of sound. Then the ratio of the apparent frequency to actual frequency of source is

• 4 : 5

• 5 : 4

• 2 : 3

• 3 : 2

When a wave travels in a medium, the particle displacement is given by the equation $\mathrm{y} = \mathrm{a} \sin 2\mathrm{\pi } \left(\mathrm{bt} - \mathrm{cx}\right)$ where a, b and c are constants. The maximum particle velocity will be twice the wave velocity, if

• $\mathrm{c} = \frac{1}{\mathrm{\pi a}}$

• $\mathrm{c} = \mathrm{\pi a}$

• b = ac

• $\mathrm{b} = \frac{1}{\mathrm{ac}}$

A progressive wave $\mathrm{y} = \mathrm{A} \sin \left(\mathrm{kx} - \mathrm{\omega t}\right)$ is reflected by a rigid wall at x = 0. Then the reflected wave can be represented by

• y = A sin (kx + ωt)

• y = A cos (kx + ωt)

• y = − A sin (kx − ωt)

• y = − A sin (kx + ωt)

A sonometer wire 100 cm long has a fundamental frequency of 330 Hz. The velocity of propagation of transverse waves on the wire is

• 330 ms^-1

• 660 ms^-1

• 990 ms^-1

• 115 ms^-1

A glass tube of length 1.0 m is completely filled with water. A vibrating tuning fork of frequency 500 Hz is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is 330 ms^-1, then the total number of resonances that occur will be

• 2

• 3

• 1

• 5

A bus is moving with a velocity of 5 ms^-1 towards a huge wall. The driver sounds a horn of frequency 165 Hz. If the speed of sound in air is 335 ms^-1, the number of beats heard per second by a passenger inside the bus will be

• 3

• 4

• 5

• 6

A train is moving at 30 ms^-1 in still air. The frequency of the locomotive whistle is 500 Hz and the speed of sound is 345 ms^-1. The apparent wavelength of sound in front of and behind the locomotive are respectively

• 0.80 m, 0.63 m

• 0.63 m, 0.80 m

• 0.50 m, 0.85 m

• 0.63 m, 0.75 m

An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is 

• 200 s^-1

• 100 s^-1

• 300 s^-1

• 250 s^-1

49.

A transverse wave is described by the equation $\mathrm{y} = {\mathrm{y}}_0 \sin 2\mathrm{\pi } \left(\mathrm{ft} - \frac{\mathrm{x}}{\mathrm{\lambda }}\right)$. The maximum particle velocity is equal to four times the wave velocity, if

• $\mathrm{\lambda } = \frac{{\mathrm{\pi y}}_0}{4}$

• $\mathrm{\lambda } = \frac{{\mathrm{\pi y}}_0}{2}$

• $\mathrm{\lambda } = {\mathrm{\pi y}}_0$

• $\mathrm{\lambda } = 2{\mathrm{\pi y}}_0$

A string of density 7.5 g cm³ and area of cross-section 0.2 mm² is stretched under a tension of 20 N. When it is plucked at the mid-point, the speed of the transverse wave on the wire is

• 116 ms^-1

• 40 ms^-1

• 200 ms^-1

• 80 ms^-1