A steel wire has a length of \(12.0\) m and a mass of \(2.10\) kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air, at \(20^{\circ}\text{C}\) (which is \(343\) m/s)?
1. \(4.3\times10^3\) N
2. \(3.2\times10^4\) N
3. \(2.06\times10^4\) N
4. \(1.2\times10^4\) N
A bat emits an ultrasonic sound of frequency \(1000\) kHz in the air. If the sound meets a water surface, what is the wavelength of the reflected sound? (The speed of sound in air is \(340\) m/sec and in water is \(1486\) m/sec)
1. \(3.4 \times 10^{-4}~\text{m}\)
2. \(1 . 49 \times 10^{- 3} ~ \text{m}\)
3. \(2 . 34 \times 10^{- 2} ~\text{m}\)
4. \(1 . 73 \times10^{- 3} ~\text{m}\)
1. | \(1.3\) m | 2. | \(3.0\) m |
3. | \(2.5\) m | 4. | \(3.5\) m |
Two sitar strings, \(A\) and \(B,\) playing the note \(Ga,\) are slightly out of tune and produce \(6~\text{Hz}\) beats. The tension in the string \(A\) is slightly reduced, and the beat frequency is found to be reduced to \(3~\text{Hz}\). If the original frequency of \(A\) is \(324~\text{Hz}\), what is the frequency of \(B\)?
1. \(316~\text{Hz}\)
2. \(318~\text{Hz}\)
3. \(319~\text{Hz}\)
4. \(314~\text{Hz}\)
1. | \(0.5~\text{s}\) | 2. | \(0.6~\text{s}\) |
3. | \(0.4~\text{s}\) | 4. | \(0.1~\text{s}\) |
A transverse wave moves from a medium \(A\) to a medium \(B\). In medium \(A\), the velocity of the transverse wave is \(500~\text{ms}^{-1}\) and the wavelength is \(5~\text{m}\). The frequency and the wavelength of the wave in medium \(B\) when its velocity is \(600~\text{ms}^{-1}\), respectively are:
1. | \(120~\text{Hz}\) and \(5~\text{m}\) | 2. | \(100~\text{Hz}\) and \(5~\text{m}\) |
3. | \(120~\text{Hz}\) and \(6~\text{m}\) | 4. | \(100~\text{Hz}\) and \(6~\text{m}\) |
A student tunes his guitar by striking a \(120~\text{Hz}\) with a tuning fork and playing the \(4^{\text{th}}\) string at the same time. By keen observation, he hears the amplitude of the combined sound oscillating thrice per second. Which of the following frequencies is most likely the frequency of the \(4^{\text{th}}\) string on his guitar?
1. \(130\)
2. \(117\)
3. \(110\)
4. \(120\)