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

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

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

## 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. $$\frac{1}{3}$$

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 $$\frac{f_1}{f_3}$$:

$$\frac{f_1}{f_3} = \frac{f_1}{3f_1} = \frac{1}{3}$$.

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. $$300 \mathrm{~Hz}$$

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

### 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 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 $\frac{\pi&space;}{2}$

C π

D  2π

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?