Q. No.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
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.
2.
3.
4.
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. \(n= \frac{n_1+ n_2+ n_3}{3}\)
| 1. | \(3\) | 2. | \(360\) |
| 3. | \(180\) | 4. | \(60\) |
1. \(1.21~\mathring{A}\)
2. \(2.42~\mathring{A}\)
3. \(0.605~\mathring{A}\)
4. \(4.84~\mathring{A}\)
1. \(3:2\)
2. \(2:3\)
3. \(9:4\)
4. \(4:9\)
| 1. | \(50~\text{cm}\) | 2. | \(60~\text{cm}\) |
| 3. | \(25~\text{cm}\) | 4. | \(20~\text{cm}\) |
The phase difference between two waves, represented by
\(y_1= 10^{-6}\sin \left\{100t+\left(\frac{x}{50}\right) +0.5\right\}~\text{m}\)
\(y_2= 10^{-6}\cos \left\{100t+\left(\frac{x}{50}\right) \right\}~\text{m}\)
where \(x\) is expressed in metres and \(t\) is expressed in seconds, is approximate:
1. \(2.07~\text{radians}\)
2. \(0.5~\text{radians}\)
3. \(1.5~\text{radians}\)
4. \(1.07~\text{radians}\)
| 1. | \({y}=0.2 \sin \left[2 \pi\left(6{t}+\frac{x}{60}\right)\right]\) |
| 2. | \({y}=0.2 \sin \left[ \pi\left(6{t}+\frac{x}{60}\right)\right]\) |
| 3. | \({y}=0.2 \sin \left[2 \pi\left(6{t}-\frac{x}{60}\right)\right]\) |
| 4. | \(y=0.2 \sin \left[ \pi\left(6{t}-\frac{x}{60}\right)\right]\) |
A steel wire \(0.72~\text{m}\) long has a mass of \(5\times10^{-3}~\text{kg}\). If the wire is under tension of \(60~\text{N}\), the speed of transverse waves on the wire will be:
1. \(85~\text{m/s}\)
2. \(83~\text{m/s}\)
3. \(93~\text{m/s}\)
4. \(100~\text{m/s}\)
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