The length of the string of a musical instrument is \(90\) cm and has a fundamental frequency of \(120\) Hz. Where should it be pressed to produce a fundamental frequency of \(180\) Hz? 

1.	\(75\) cm	2.	\(60\) cm
3.	\(45\) cm	4.	\(80\) cm

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. \(2\pi\)

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

For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?
1. \(\pi y_0\)
2. \(2\pi y_0\)
3. \(\pi y_0/2\)
4. \(4\pi y_0\)

Two stationary sources exist, each emitting waves of wavelength λ. If an observer moves from one source to the other with velocity u, then the number of beats heard by him is equal to:

1. $\frac{2u}{\lambda }$

2. $\frac{u}{\lambda }$

3. $\sqrt{\mu \lambda }$

4. $\frac{\mu }{2\lambda }$

A string is cut into three parts, having fundamental frequencies n₁, n₂, and n₃ respectively. The original fundamental frequency "n" is related by the expression:

1. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

2. $n=n_1\times n_2\times n_3$

3. $n=n_1+n_2+n_3$

4. $n=\frac{n_1+n_2+n_3}{3}$

The equations of two waves are given as x = acos(ωt + δ) and y = a cos (ωt + $\alpha$), where δ = $\alpha$ + $\pi$/2, then the resultant wave can be represented by:

1. a circle (c.w)

2. a circle (a.c.w)

3. an ellipse (c.w)

4. an ellipse (a.c.w)

Two vibrating tuning forks produce progressive waves given by \(Y_1 = 4 ~\mathrm{sin}~500 \pi \mathrm{t}\) and \(Y_2 = 2 ~\mathrm{sin}~506 \pi \mathrm{t}\). The number of beats produced per minute is:

If a standing wave having 3 nodes and 2 antinodes is formed within 1.21 Å distance, then the wavelength of the standing wave will be:
1.  1.21 Å
2.  2.42 Å
3.  0.605 Å
4.  4.84 Å

A point source emits sound equally in all directions in a non-absorbing medium. Two points, P and Q, are at distances of \(2\) m and \(3\) m, respectively, from the source. The ratio of the intensities of the waves at P and Q is:
1. \(3:2\)
2. \(2:3\)
3. \(9:4\)
4. \(4:9\)