**IBDP Physics SL 2025 – C.4 Standing waves and resonance SL Paper 1 Exam Style Questions **

## IBDP Physics 2025 SL Paper 1 – All Chapters

## Topic: C.4 Standing waves and resonance SL Paper 1

Standing Waves, Vibrating Strings, Vibrating Air Columns, Resonance, Damping

## Question -C.4 Standing waves and resonance SL Paper 1

A standing wave with a first harmonic of frequency \(f_1\) is formed on a string fixed at both ends.

The frequency of the third harmonic is \(f_3\).

What is \(\frac{f_1}{f_3}\) ?

A. 3

B. \(\frac{3}{2}\)

C. \(\frac{2}{3}\)

D. \(\frac{1}{3}\)

**▶️Answer/Explanation**

Ans:D

In a standing wave on a string fixed at both ends, the frequencies of the harmonics are related as follows:

- The frequency of the first harmonic (\(f_1\)) is the fundamental frequency.
- The frequency of the nth harmonic is given by \(f_n = nf_1\).

So, the frequency of the third harmonic (\(f_3\)) is:

\(f_3 = 3f_1\).

Now, we can find \(\frac{f_1}{f_3}\):

\(\frac{f_1}{f_3} = \frac{f_1}{3f_1} = \frac{1}{3}\).

So, the correct answer is:

D. \(\frac{1}{3}\).

#### Question

A pipe containing air is closed at one end and open at the other. The third harmonic standing wave for this pipe has a frequency of \(150 \mathrm{~Hz}\).

What other frequency is possible for a standing wave in this pipe?

A. \(25 \mathrm{~Hz}\)

B. \(50 \mathrm{~Hz}\)

C. \(75 \mathrm{~Hz}\)

D. \(300 \mathrm{~Hz}\)

**▶️Answer/Explanation**

Ans:B

In a closed-open pipe (like an open-end organ pipe), the fundamental frequency (first harmonic) is produced when the length of the pipe is one-fourth (1/4) of the wavelength of the sound wave. In this case, the pipe is closed at one end and open at the other.

The third harmonic has a frequency of \(150 \, \text{Hz}\), which means that the pipe length corresponds to one and a half wavelengths (\(\lambda/2\)). The fundamental frequency (\(f_1\)) corresponds to a quarter-wavelength (\(\lambda/4\)).

So, if the third harmonic is at \(150 \, \text{Hz}\), we can find the fundamental frequency (\(f_1\)) as follows:

\(\frac{f_3}{f_1} = \frac{\lambda_3}{\lambda_1} = \frac{3}{1}\)

\(f_1 = \frac{f_3}{3} = \frac{150 \, \text{Hz}}{3} = 50 \, \text{Hz}\)

Therefore, the possible frequency for a standing wave in this pipe, other than the third harmonic, is the fundamental frequency, which is \(50 \, \text{Hz\).

*Question*

The frequency of the first harmonic standing wave in a pipe that is open at both ends is 200 Hz. What is the frequency of the first harmonic in a pipe of the same length that is open at one end and closed at the other?

A. 50 Hz

B. 75 Hz

C. 100 Hz

D. 400 Hz

**Answer/Explanation**

### Markscheme

C

For Pipe Open at both Ends

\(L=n{}’\frac{\lambda}{2}\)

\(v= f \lambda\)

or

\(f=\frac{v}{\lambda}=\frac{n{}’}{2L} \times v\)

For first harmonic \(n{}’ =1 \)

\(f_{1(n=1)}=\frac{1}{2L}v =200\; Hz\) —-(1)

For Pipe closed at one end

\(L=(2n+1)\frac{\;\lambda}{4} \; where \; n=0,1,2,3 \; etc..\)

\(\because v=f\lambda\)

\(\therefore f=\frac{v}{\lambda}=\frac{2n+1}{4L}\times v\)

\(f_{2(n=0)}=\frac{1}{4L}v\) —-(2)

From eq^{n} (1) and (2) We get

\(f_{2(n=0)} =100\; Hz\)

*Question*

The air in a pipe, open at both ends, vibrates in the second harmonic mode.

P Q

What is the phase difference between the motion of a particle at P and the motion of a particle at Q?

A 0

B

C π

D 2π

**Answer/Explanation**

Answer – C

For an open organ pipe, the length L is given as

\(L=n\frac{\Lambda }{2}\)

where, λ is the wavelength of wave and n is an integer and by putting n = 1,2,3,…………… we get the modes of vibration.

n=1 gives first harmonics, n=2 gives second harmonics and so on.

Here, an open organ pipe of length L vibrates in second harmonic mode,

hence the length of pipe is

\(L=\frac{2\Lambda }{2}=\Lambda\)

\(L=\Lambda\)

And P and Q at \(\frac{\Lambda }{2}\)

Phase difference \(=\frac{2\pi }{\Lambda }\left ( \Delta x \right )\) path difference.

Which is equal to \(\pi \)

Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

**Answer/Explanation**

### Markscheme

**A**