When a string is divided into three segments of lengths \(l_1\), \(l_2\) and \(l_3\), the fundamental frequencies of these three segments are \(\nu_1\), \(\nu_2\) and \(\nu_3\) respectively. The original fundamental frequency (\(\nu\)) of the string is:
1. \(\sqrt{\nu} = \sqrt{\nu_1}+\sqrt{\nu_2}+\sqrt{\nu_3}\)
2. \(\nu = \nu_1+\nu_2+\nu_3\)
3. \(\frac{1}{\nu} =\frac{1}{\nu_1} +\frac{1}{\nu_2}+\frac{1}{\nu_3}\)
4. \(\frac{1}{\sqrt{\nu}} =\frac{1}{\sqrt{\nu_1}} +\frac{1}{\sqrt{\nu_2}}+\frac{1}{\sqrt{\nu_3}}\)
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 |
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
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 \(5.0~\text{m}\) and \(5.5~\text{m}\), respectively, propagate in gas with a velocity of \(330~\text{m/s}\). How many beats per second can we expect?
1. \(12\)
2. \(0\)
3. \(1\)
4. \(6\)