IB Physics Standing waves and resonance Practice Questions

Q: A string fixed at both ends has a fundamental frequency of $100\,\text{Hz}$. What is the frequency of its third harmonic?

$300\,\text{Hz}$. Harmonics of a string are integer multiples of the fundamental: third harmonic $=3\times 100=300\,\text{Hz}$.

Question 1

A point of zero amplitude on a standing wave is called a:

Accepted Answer

Node. A node is a point of permanently zero amplitude, formed by destructive interference of the two travelling waves.

Question 2

A string of length $L$ fixed at both ends vibrates at its fundamental frequency. The wavelength is:

Accepted Answer

$2L$. The fundamental has a node at each end and one antinode, so $L=\frac{\lambda}{2}$, giving $\lambda=2L$.

Question 3

A pipe closed at one end and open at the other resonates at a fundamental wavelength of:

Accepted Answer

$4L$. A closed pipe has a node at the closed end and antinode at the open end, so $L=\frac{\lambda}{4}$, giving $\lambda=4L$.

Question 4

A point of maximum amplitude on a standing wave is called a(n):

Accepted Answer

Antinode. An antinode is a point of maximum oscillation amplitude, halfway between adjacent nodes.

Question 5

A string fixed at both ends has a fundamental frequency of $100\,	ext{Hz}$. What is the frequency of its third harmonic?

Accepted Answer

$300\,	ext{Hz}$. Harmonics of a string are integer multiples of the fundamental: third harmonic $=3	imes 100=300\,	ext{Hz}$.

Question 6

Resonance occurs when a system is driven at a frequency equal to its:

Accepted Answer

Natural frequency. A system resonates, with large amplitude, when driven at its natural frequency.

Question 7

On a standing wave, a point that never moves is called a _____.

Accepted Answer

node. A node has permanently zero displacement; adjacent nodes are half a wavelength apart.

Question 8

For a string of length $L$ fixed at both ends, the fundamental standing wave has a wavelength of _____ (in terms of $L$).

Accepted Answer

2L / 2*L / 2l. The fundamental fits half a wavelength on the string, so $\lambda=2L$.

Question 9

A pipe open at both ends of length 0.40 m has a first harmonic of frequency f. A pipe open at one end and closed at the other has the same first harmonic f. What is the length of the second pipe?

Accepted Answer

0.20 m. An open pipe first harmonic has wavelength 2L; a closed pipe first harmonic has wavelength 4L. For the same frequency (same wavelength), 4 L_closed = 2 x 0.40, so L_closed = 0.20 m.

Question 10

A pipe closed at one end has a closed end that must be a

Accepted Answer

displacement node. displacement node.

IB Physics: Standing waves and resonance — Practice Questions & Answers

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