A wave traveling in the +ve \(x\)-direction having maximum displacement along \(y\)-direction as \(1~\text{m}\), wavelength \(2\pi ~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
1. \(y=\sin (2 \pi x-2 \pi t)\)
2. \(y=\sin (10 \pi x-20 \pi t)\)
3. \(y=\sin (2 \pi x+2 \pi t)\)
4. \( y=\sin (x-2 t)\)
Two sources of sound placed close to each other, are emitting progressive waves given by,
\(y_1=4\sin 600\pi t\) and \(y_2=5\sin 608\pi t\).
An observer located near these two sources of sound will hear:
1. | \(4\) beats per second with intensity ratio \(25:16\) between waxing and waning |
2. | \(8\) beats per second with intensity ratio \(25:16\) between waxing and waning |
3. | \(8\) beats per second with intensity ratio \(81:1\) between waxing and waning |
4. | \(4\) beats per second with intensity ratio \(81:1\) between waxing and waning |
Two waves are represented by the equations and
,
where \(x\) is in metres and \(t\) in seconds. The phase difference between them is:
1. \(1.25\) rad
2. \(1.57\) rad
3. \(0.57\) rad
4. \(1.0\) rad
Sound waves travel at \(350\) m/s through warm air and at \(3500\) m/s through brass. The wavelength of a \(700\) Hz acoustic wave as it enters brass from warm air:
1. | increase by a factor of \(20\) |
2. | increase by a factor of \(10\) |
3. | decrease by a factor of \(20\) |
4. | decrease by a factor of \(10\) |
A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1. A/2
2. A
3. 2A
4. A
A tuning fork of frequency \(512\) Hz makes \(4\) beats/s with the vibrating string of a piano. The beat frequency decreases to \(2\) beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:
1. \(510\) Hz
2. \(514\) Hz
3. \(516\) Hz
4. \(508\) Hz
A wave in a string has an amplitude of 2 cm. The wave travels in the positive direction of the x-axis with a speed of 128 m/s and it is noted that 5 complete waves fit in the 4 m length of the string. The equation describing the wave is:
1. | y = (0.02)m sin(7.85x+1005t) |
2. | y = (0.02)m sin(15.7x -2010t) |
3. | y = (0.02)m sin(15.7x+2010t) |
4. | y = (0.02)m sin(7.85x -1005t) |
Each of the two strings of lengths 51.6 cm and 49.1 cm is tensioned separately by 20 N of force. The mass per unit length of both strings is the same and equals 1 g/m. When both the strings vibrate simultaneously, the number of beats is:
1. | 5 | 2. | 7 |
3. | 8 | 4. | 3 |
The wave described by \(y=0.25\sin (10\pi x-2\pi t)\), where \(x \) and \(y\) are in metre and \(t\) in second, is a wave travelling along the:
1. | \(1\) Hz | –ve x-direction with frequency
2. | \(\pi\) Hz and wavelength \(\lambda=0.2\) m | +ve x-direction with frequency
3. | \(1\) Hz and wavelength \(\lambda=0.2\) m | +ve x-direction with frequency
4. | \(0.25\) m and wavelength \(\lambda=0.2\) m | –ve x-direction with amplitude
Two sound waves with wavelengths 5.0 m and 5.5 m, respectively, propagate in gas with a velocity of 330 m/s. How many beats per second can we expect?
1. 12
2. 0
3. 1
4. 6