Two identical piano wires, kept under the same tension T, have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both the wires oscillate together would be:
1. 0.01
2. 0.02
3. 0.03
4. 0.04
The equation of a simple harmonic wave is given by \(y=3\sin \frac{\pi}{2}(50t-x)\) where \(x \) and \(y\) are in meters and \(t\) is in seconds. The ratio of maximum particle velocity to the wave velocity is:
1. \(\frac{3\pi}{2}\)
2. \(3\pi\)
3. \(\frac{2\pi}{3}\)
4. \(2\pi\)
Which one of the following statements is true?
1. | Both light and sound waves in the air are transverse. |
2. | The sound waves in the air are longitudinal while the light waves are transverse. |
3. | Both light and sound waves in the air are longitudinal. |
4. | Both light and sound waves can travel in a vacuum. |
The time of reverberation of a room \(A\) is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double those of room A?
1. 2
2. 4
3.
4. 1
A transverse wave propagating along the x-axis is represented by:
\(y=(x,t)=8.0\mathrm{sin}(0.5\pi x-4\pi t-\frac{\pi}{4})\) where \(x\) is in meters and \(t\) in seconds. The speed of the wave is:
1. \(4\pi\) m/s
2. \(0.5\) m/s
3. \(\frac{\pi}{4}\) m/s
4. \(8\) m/s
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
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
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 |