C.4 Standing waves and resonance SL Paper 1 - IBDP Physics 2025 SL

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

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 eqⁿ (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 $\frac{\pi }{2}$

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 $

Question

Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

Answer/Explanation