### Question 1

**Which of the following best describes a standing wave?**

A. A wave that travels in one direction only

B. A wave that is formed by the superposition of two waves travelling in opposite directions

C. A wave that does not have any nodes or antinodes

D. A wave that always has a constant frequency and amplitude

### Question 2

**In a standing wave, what is the phase difference between particles at a node and an antinode?**

A. 0 degrees

B. 90 degrees

C. 180 degrees

D. 360 degrees

### Question 3

**Which of the following is NOT a characteristic of nodes in a standing wave?**

A. Maximum amplitude

B. No displacement

C. Points of destructive interference

D. Remain stationary

### Question 4

**How are antinodes formed in a standing wave?**

A. By destructive interference of two waves

B. Where the amplitude of the wave is zero

C. By constructive interference of two waves

D. Where the wave speed is maximum

### Question 5

**If the distance between two consecutive nodes in a standing wave is 25 cm, what is the wavelength of the wave?**

A. 25 cm

B. 50 cm

C. 75 cm

D. 100 cm

### Question 6

**a) **Explain how standing waves are formed when two waves of the same frequency and amplitude travel in opposite directions in a medium. [3]

**b)** A string of length 1.2 m is fixed at both ends and is made to vibrate in its second harmonic. Calculate the wavelength of the standing wave formed. [2]

### Question 7

**a)** Define the terms 'node' and 'antinode' in the context of standing waves. [2]

**b) **A pipe open at both ends produces a standing wave with a frequency of 440 Hz. If the speed of sound in air is 340 m/s, determine the length of the pipe. [3]

### Question 8

**a)** Describe the difference in the formation of standing waves in a pipe that is closed at one end compared to a pipe that is open at both ends. [3]

**b)** A pipe closed at one end has a length of 0.5 m. If the speed of sound in air is 340 m/s, calculate the fundamental frequency of the standing wave produced in the pipe. [2]

### Question 9

**a)** How does the length of a pipe affect the frequency of the standing wave produced when it is closed at one end? [2]

**b)** A pipe closed at one end has a length of 0.75 m. If the speed of sound in air is 340 m/s, calculate the first three harmonics of the standing wave produced in the pipe. [4]

**c)** Explain why a pipe closed at one end does not produce even harmonics. [2]

### Question 10

**a) **Describe the difference between the first and second harmonics in a pipe that is open at both ends. [3]

**b)** If the second harmonic in a pipe open at both ends has a frequency of 256 Hz and the speed of sound in air is 340 m/s, determine the length of the pipe. [3]

**c)** Explain why increasing the diameter of the pipe does not significantly affect the frequency of the standing wave produced. [2]

### Question 11

**Which of the following best describes the motion of particles at an antinode in a standing wave?**

A. They remain stationary

B. They oscillate with maximum amplitude

C. They oscillate with minimum amplitude

D. They move in the direction of wave propagation

### Question 12

**In a pipe closed at one end, where is the node located?**

A. At the open end

B. At the closed end

C. At both ends

D. Neither at the open nor at the closed end

### Question 13

**Which of the following is true regarding the frequency of a standing wave?**

A. It is always zero

B. It is the same as the frequency of the individual waves that interfere to produce it

C. It is the sum of the frequencies of the individual waves

D. It is the difference between the frequencies of the individual waves

### Question 14

**What happens to the pattern of nodes and antinodes when the frequency of a standing wave increases?**

A. The number of nodes and antinodes remains the same

B. The number of nodes and antinodes decreases

C. The number of nodes and antinodes increases

D. Only the number of nodes increases

### Question 15

**In a standing wave on a string fixed at both ends, if there are 3 nodes (including the fixed ends), how many antinodes are there?**

A. 1

B. 2

C. 3

D. 4

### Question 16

**a)** What is meant by 'end effects' in the context of standing waves in pipes? [2]

**b)** A flute, which is essentially a pipe open at both ends, produces a note with a frequency of 440 Hz. If the speed of sound in air is 340 m/s, calculate the effective length of the flute. [3]

**c)** Describe how a musician can change the frequency of the note produced by a flute without changing its length. [3]

### Question 17

**a)** How does the frequency of a standing wave change if the tension in the medium (e.g., a string) is increased? [2]

**b)** A string of length 0.65 m is made to vibrate in its third harmonic. If the speed of waves on the string is 260 m/s, determine the frequency of the standing wave. [3]

**c)** Explain the role of nodes and antinodes in the formation of standing waves on a string. [3]

### Question 18

**a)** Describe how standing waves are formed on a string when it is plucked or struck. [3]

**b) **A string of length 1.2 m is fixed at both ends. If it vibrates in its second harmonic with a frequency of 50 Hz, calculate the speed of the wave on the string. [3]

**c)** How does increasing the mass per unit length (linear density) of the string affect the frequency of the standing wave produced? [2]

**d)** If the linear density of the string is doubled while keeping the tension constant, determine the new frequency when it vibrates in its second harmonic. [3]

### Question 19

**a) **Define nodes and antinodes in the context of standing waves on a string. [2]

**b) **A string of length 0.8 m vibrates in its third harmonic. Calculate the distance between two consecutive nodes. [3]

**c)** How many antinodes will be present on the string when it vibrates in its third harmonic? [2]

**d)** If the tension in the string is increased, how will it affect the positions of nodes and antinodes? [2]

### Question 20

**a)** Explain the significance of the fundamental frequency in the context of standing waves on a string. [3]

**b) **A string of length 1.5 m has a fundamental frequency of 40 Hz. Calculate the speed of the wave on the string. [3]

**c) **If the string is shortened to a length of 1 m while keeping all other factors constant, determine the new fundamental frequency. [3]

**d)** Describe how the pattern of nodes and antinodes changes when the string moves from its fundamental frequency to its second harmonic. [2]