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

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

IBDP Physics SL Paper 1 -FA 2025- All Chapters

Question

A pipe of length 0.75 m is closed at one end. Sound speed is 330 m/s. What are the first two harmonic frequencies?
(A) 110 Hz and 220 Hz
(B) 110 Hz and 330 Hz
(C) 220 Hz and 440 Hz
(D) 220 Hz and 660 Hz
▶️ Answer/Explanation
Detailed solution

For closed pipe: L = λ/4, 3λ/4, 5λ/4,… (odd harmonics only)
Fundamental: λ = 4L = 4 × 0.75 = 3.0 m
f₁ = v/λ = 330/3.0 = 110 Hz
Third harmonic: f₃ = 3f₁ = 330 Hz
✅ Answer: (B) 110 Hz and 330 Hz

Question

A standing wave with a first harmonic of frequency \(f_1\) is formed on a string fixed at both ends.
Standing wave on a string (fixed ends)
The frequency of the third harmonic is \(f_3\).
What is \(\dfrac{f_1}{f_3}\) ?
A. \(3\)
B. \(\dfrac{3}{2}\)
C. \(\dfrac{2}{3}\)
D. \(\dfrac{1}{3}\)
▶️Answer/Explanation

✅ Answer: D

For a string fixed at both ends, the harmonic frequencies follow
\(f_n = n f_1\).

So, for the third harmonic:
\(f_3 = 3f_1\).

Therefore,
\(\dfrac{f_1}{f_3} = \dfrac{f_1}{3f_1} = \dfrac{1}{3}\).

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 \(150\,\text{Hz}\).
What other frequency is possible for a standing wave in this pipe?
A.  \(25\,\text{Hz}\)
B.  \(50\,\text{Hz}\)
C.  \(75\,\text{Hz}\)
D.  \(300\,\text{Hz}\)
▶️ Answer/Explanation
Detailed solution

For a pipe closed at one end and open at the other, only odd harmonics are present. The harmonic frequencies are given by \[ f_n = n f_1 \quad \text{where } n = 1, 3, 5, \dots \]

The third harmonic has frequency \[ f_3 = 3 f_1 = 150\,\text{Hz}. \] Hence, \[ f_1 = \frac{150}{3} = 50\,\text{Hz}. \]

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

✅ Answer: (B)

More C.4 Standing waves and resonance SL Paper 1 Questions..
Scroll to Top