Home / IBDP Physics- C.4 Standing waves and resonance- IB Style Questions For HL Paper 1A

IBDP Physics- C.4 Standing waves and resonance- IB Style Questions For HL Paper 1A -FA 2025

IBDP Physics HL Paper 1 -FA 2025- All Chapters

Question 

A string that is fixed at both ends oscillates in the second harmonic with frequency \(100\,\mathrm{Hz}\).

What other harmonic frequencies, in \(\mathrm{Hz}\), can this string oscillate at?

(A) \(25\) and \(50\)
(B) \(25\) and \(75\)
(C) \(50\) and \(150\)
(D) \(75\) and \(150\)
▶️ Answer/Explanation

Correct Answer: \( \boxed{\mathrm{C}} \)

For a string fixed at both ends, the harmonic frequencies are integer multiples of the fundamental frequency:

\(f_n=nf_1\)

The second harmonic has frequency

\(f_2=2f_1=100\,\mathrm{Hz}\)

Therefore, the fundamental frequency is

\(f_1=\dfrac{100}{2}=50\,\mathrm{Hz}\)

The third harmonic is

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

Thus, the other harmonic frequencies listed are \(50\,\mathrm{Hz}\) and \(150\,\mathrm{Hz}\).

Hence, the correct answer is \( \boxed{\mathrm{C}} \).

Question 

A standing sound wave is formed in a pipe of length \(L\) that is open at both ends. The standing wave has two nodes. What is the wavelength of the standing wave?

(A) \(\frac{L}{2}\)
(B) \(\frac{2L}{3}\)
(C) \(L\)
(D) \(2L\)
▶️ Answer/Explanation

Correct Answer: \( \boxed{\mathrm{C}} \)

For a pipe open at both ends, both ends are displacement antinodes.

A standing wave with two nodes corresponds to the second harmonic. For an open pipe, the allowed wavelengths satisfy

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

For two nodes, \(n=2\). Therefore,

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

Hence,

\(\lambda=L\)

Thus, the wavelength of the standing wave is

\( \boxed{\lambda=L} \)

Hence, the correct answer is \( \boxed{\mathrm{C}} \).

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
Detailed solution

For a pipe that is closed at one end and open at the other, only odd harmonics are present.

The allowed harmonic frequencies are given by:

\( f_n = (2n – 1)f_1 \quad \text{where } n = 1,2,3,\dots \)

The third harmonic corresponds to:

\( f_3 = 3f_1 \)

Given \( f_3 = 150\,\mathrm{Hz} \),

\( f_1 = \dfrac{150}{3} = 50\,\mathrm{Hz} \)

Therefore, another possible standing-wave frequency in this pipe is the fundamental frequency of \(50\,\mathrm{Hz}\).

✅ Answer: (B)

More DP Physics HL Paper 1 Questions..
Scroll to Top