The equation of a stationary wave is given as where t is in seconds and x in centimetres. Which of the following is correct?
1. | Wavelength of the component waves is 10 cm. |
2. | The separation between a node and the nearest antinode is 2.5 cm. |
3. | Frequency of the component wave is 0.25 Hz. |
4. | All of these |
A standing wave is represented by where Y and A are in millimetres, t is in seconds and x is in metres. The velocity of the wave is:
1. | 104 m/s |
2. | 1 m/s |
3. | 10–4 m/s |
4. | Not derivable from the above data |
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.
2.
3.
4.
A string of length l is fixed at one end and free at the other. If it resonates in different modes, then the ratio of frequencies is:
1. 1:2:3: ......
2. 1:3:5:7: ......
3. 1:2:4:8: ..........
4. 1:3:9: ........
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 fundamental frequency of an open organ pipe is 200 Hz. If one end of the pipe is closed, its fundamental frequency becomes:
1. | 100 Hz | 2. | 200 Hz |
3. | 50 Hz | 4. | 400 Hz |
An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is \(50\) cm. The next larger length of the column resonating with the same tuning fork will be:
1. | \(100\) cm | 2. | \(150\) cm |
3. | \(200\) cm | 4. | \(66.7\) cm |
The equation of a stationary wave is \(y = 0.8 ~cos\left(\frac{\pi x}{20}\right)sin200(\pi t)\), where \(x\) is in cm and \(t\) is in sec. The separation between consecutive nodes will be:
1. \(20~\text{cm}\)
2. \(10~\text{cm}\)
3. \(40~\text{cm}\)
4. \(30~\text{cm}\)
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