When sound is produced in an aeroplane moving with a velocity of 200 m/s horizontal its echo is heard after 10$\sqrt{5}$ s. If velocity of sound in air is 300 ms^-1 the elevation of aircraft is

• 250 m

• $250\sqrt{5} \mathrm{m}$

• 1250 m

• 2500 m

Two tuning forks of frequency n₁ and n₂ produces n beats per second. If n₁ and n₂ are known, n₁ may be given by

• $\frac{{\mathrm{n}}_2}{\mathrm{n}} + {\mathrm{n}}_2$

• n₂n

• n₂ ± n

• $\frac{{\mathrm{n}}_2}{\mathrm{n}} - {\mathrm{n}}_2$

A car moving with a velocity of 36 km/h crosses a siren of frequency 500 Hz. The apparent frequency of siren after passing it will be

• 520 Hz

• 485 Hz

• 540 Hz

• 460 Hz

The equation of a progressive wave is$\mathrm{y} = 4 \sin (4\mathrm{\pi t} - 0.04\mathrm{x} + \mathrm{\pi }/3)$ where x is in metre and t is in second. The velocity of the wave is

• $100 \mathrm{\pi } \mathrm{m}/\mathrm{s}$

• $50 \mathrm{\pi } \mathrm{m}/\mathrm{s}$

• $25 \mathrm{\pi } \mathrm{m}/\mathrm{s}$

• $\mathrm{\pi } \mathrm{m}/\mathrm{s}$

A longitudinal wave is represented by $\mathrm{x} = {\mathrm{x}}_0 \sin 2\mathrm{\pi } (\mathrm{nt} - \mathrm{x}/\mathrm{\lambda })$. The maximum particle velocity will be four times the wave velocity if

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

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

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

• $\mathrm{\lambda } = 4{\mathrm{\pi x}}_0$

A plane progressive wave is given by y = 2 cos 6.284 (330t − x). What is the period of the wave ? 

• $\frac{1}{330} \mathrm{s}$

• $2 \mathrm{\pi } \times 330 \mathrm{s}$

• ${\left(2\mathrm{\pi } \times 330\right)}^{-1} \mathrm{s}$

• $\frac{6.284}{330} \mathrm{s}$

A train approaching a railway platform with a speed of 20 ms^-1 starts blowing the whistle. Speed of sound in air is 340 ms^-1. If the frequency of the emitted sound from the whistle is 640 Hz, the frequency of sound to a person standing on the platform will appear to be

• 600 Hz

• 640 Hz

• 680 Hz

• 720 Hz

The frequency of the first overtone of a closed pipe of length l₁ is equal to that of the first overtone of an open pipe of length l₂. The ratio of their lengths (l₁ : l₂) is

• 2 : 3

• 4 : 5

• 3 : 5

• 3 : 4

A progressive wave moving along x-axis is represented by $\mathrm{y} = \mathrm{A}\hspace{0.17em}\sin \left[\frac{2\mathrm{\pi }}{\mathrm{\lambda }}(\mathrm{vt} - \mathrm{x})\right]$. The wavelength (λ) at which the maximum particle velocity is 3 times the wave velocity is

• A/3

• 2A/(3π)

• $\left(\frac{3}{4}\right)\mathrm{\pi A}$

• (2/3) πA

280.

A wave travelling in the positive x-direction having displacement along y-direction as 1 m, wavelength 2$\mathrm{\pi }$ m and frequency of $\frac{1}{\mathrm{\pi }}$ Hz is represented by

• y = sin (x − 2t)

• $\mathrm{y} = \sin (2\mathrm{\pi x} - 2\mathrm{\pi t})$

• $y = \sin (10\mathrm{\pi x} - 20\mathrm{\pi t})$

• $\mathrm{y} = \sin (2\mathrm{\pi x} + 2\mathrm{\pi t})$