Resonance of sound wave – problems and solutions

1. After the tuning fork A is vibrated, the tuning fork B is vibrated. The tuning fork B is vibrated because…..

A. The tuning fork A has the same amplitude as the tuning fork B

Resonance of sound wave - problems and solutions 1

B. Both tuning forks use the same resonance box

C. The tuning fork B has the same frequency as the tuning fork A

D. The timbre of the sounds caused by both tuning forks are the same

Solution

After vibrated, the tuning fork A vibrates the air around it so the air also vibrates with the same frequency. Furthermore, the air vibrates the tuning fork B. The tuning fork B is also vibrating with natural frequency but the amplitude of the vibration is very small and the vibration is not visible. Since the natural frequency of the tuning fork B is equal to the frequency of the air vibration and the frequency of the tuning fork A, then the air molecule amplifies the amplitude of the tuning fork B. The tuning fork B appears to vibrate because its amplitude of vibration is visible.

The correct answer is C.

2. A resonance tube produces a loud sound for the first time when the length of the air column is 17 cm and a loud sound at the second time when the length of the air column is 51 cm. The tuning fork frequency used is 500 Hz. Determine the speed of the air in the tube.

A. 138 m/s

B. 230 m/s

C. 340 m/s

D. 461 m/s

Solution :

The shape of the resonance tube is one end is open, and the other end is closed so the distance between the node and anti-node = the minimum length of tube = ¼ λ = λ / 4.

The equation of the length of the tube :

Resonance of sound wave - problems and solutions 2

The distance between the node and an anti-node of the tube of resonance with one end is open, and another end is closed, fulfilled when n is an odd number

Resonance of sound wave - problems and solutions 3

Resonance of sound wave - problems and solutions 4

The correct answer is C.

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3. The first resonance in the tube of resonance occurs when the length of the air column is 20 cm. The second resonance and the third resonance happen when the length of the air column is…

A. 40 cm and 60 cm

B. 30 cm and 40 cm

C. 60 cm and 100 cm

D. 100 cm and 200 cm

Known :

The length of the air column if n1 = 1 (L1) = 0.2 m

Wanted : The length of the air column if n2 = 3 and n3 = 5

Solution :

The equation of the length of the tube (equation of the length of air column) :

Resonance of sound wave - problems and solutions 5

Use this equation to calculate the wavelength using the above data :

Resonance of sound wave - problems and solutions 6

The length of the air column when n2 = 3 :

Resonance of sound wave - problems and solutions 7

The correct answer is C.

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