Advertisements
Advertisements
प्रश्न
The equation \[y = A \sin^2 \left( kx - \omega t \right)\]
represents a wave motion with
विकल्प
amplitude A, frequency \[\omega/2\pi\]
amplitude A/2, frequency \[\omega/\pi\]
amplitude 2A, frequency \[\omega/4\pi\]
does not represent a wave motion.
Advertisements
उत्तर
amplitude A/2, frequency \[\omega/\pi\]
\[y = A \sin^2 \left( kx - \omega t \right)\]
\[\left[ \cos^2 \theta = 1 - 2 \sin^2 \theta \sin^2 \theta = \frac{1 - \cos^2 \theta}{2} \right]\]
\[y = A\left[ \frac{1 - \cos^2 \left( kx - \omega t \right)}{2} \right]\]
\[y = \frac{A}{2}\left[ 1 - \cos^2 \left( kx - \omega t \right) \right]\]
Thus, we have:
Amplitude = \[\frac{A}{2}\]
\[2\left( \frac{\omega}{2\pi} \right) = \frac{\omega}{\pi}\]
APPEARS IN
संबंधित प्रश्न
Explain what is Doppler effect in sound
The wavelengths of two sound waves in air are `81/173`m and `81/170`m. They produce 10 beats per second. Calculate the velocity of sound in air
Can you hear your own words if you are standing in a perfect vacuum? Can you hear your friend in the same conditions?
The voice of a person, who has inhaled helium, has a remarkably high pitch. Explain on the basis of resonant vibration of vocal cord filled with air and with helium.
When sound wave is refracted from air to water, which of the following will remain unchanged?
When two waves with same frequency and constant phase difference interfere,
An electrically maintained tuning fork vibrates with constant frequency and constant amplitude. If the temperature of the surrounding air increases but pressure remains constant, the produced will have
(a) larger wavelength
(b) larger frequency
(c) larger velocity
(d) larger time period.
The fundamental frequency of a vibrating organ pipe is 200 Hz.
(a) The first overtone is 400 Hz.
(b) The first overtone may be 400 Hz.
(c) The first overtone may be 600 Hz.
(d) 600 Hz is an overtone.
Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (1.0 × 105 ± 14) Pa and the particles of the air vibrate in simple harmonic motion of amplitude 5.5 × 10−6 m.
The sound level at a point 5.0 m away from a point source is 40 dB. What will be the level at a point 50 m away from the source?
A string, fixed at both ends, vibrates in a resonant mode with a separation of 2⋅0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1⋅6 cm. Find the length of the string.
A particular guitar wire is 30⋅0 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes?
Two speakers S1 and S2, driven by the same amplifier, are placed at y = 1.0 m and y = −1.0 m(See figure). The speakers vibrate in phase at 600 Hz. A man stands at a point on the X-axis at a very large distance from the origin and starts moving parallel to the Y-axis. The speed of sound in air is 330 m s−1. (a) At what angle θ will the intensity of sound drop to a minimum for the first time? (b) At what angle will he hear a maximum of sound intensity for the first time? (c) If he continues to walk along the line, how many more can he hear?
Two coherent narrow slits emitting sound of wavelength λ in the same phase are placed parallel to each other at a small separation of 2λ. The sound is detected by moving a detector on the screen ∑ at a distance D(>>λ) from the slit S1 as shown in figure. Find the distance x such that the intensity at P is equal to the intensity at O.
Show that if the room temperature changes by a small amount from T to T + ∆T, the fundamental frequency of an organ pipe changes from v to v + ∆v, where \[\frac{∆ v}{v} = \frac{1}{2}\frac{∆ T}{T} .\]
Two electric trains run at the same speed of 72 km h−1 along the same track and in the same direction with separation of 2.4 km between them. The two trains simultaneously sound brief whistles. A person is situated at a perpendicular distance of 500 m from the track and is equidistant from the two trains at the instant of the whistling. If both the whistles were at 500 Hz and the speed of sound in air is 340 m s−1, find the frequencies heard by the person.
A train running at 108 km h−1 towards east whistles at a dominant frequency of 500 Hz. Speed of sound in air is 340 m/s. What frequency will a passenger sitting near the open window hear? (b) What frequency will a person standing near the track hear whom the train has just passed? (c) A wind starts blowing towards east at a speed of 36 km h−1. Calculate the frequencies heard by the passenger in the train and by the person standing near the track.
A person standing on a road sends a sound signal to the driver of a car going away from him at a speed of 72 km h−1. The signal travelling at 330 m s−1 in air and having a frequency of 1600 Hz gets reflected from the body of the car and returns. Find the frequency of the reflected signal as heard by the person.
Figure shows a source of sound moving along X-axis at a speed of 22 m s−1continuously emitting a sound of frequency 2.0 kHz which travels in air at a speed of 330 m s−1. A listener Q stands on the Y-axis at a distance of 330 m from the origin. At t = 0, the sources crosses the origin P. (a) When does the sound emitted from the source at P reach the listener Q? (b) What will be the frequency heard by the listener at this instant? (c) Where will the source be at this instant?
