Q1. Two tuning forks of 256 Hz and 260 Hz are sounded together. Find the beat frequency.
f_beat = |f₁ − f₂|
f_beat = |256 − 260|
f_beat = 4 Hz (4 beats per second)
Waves — Class 11
Sound, light and ripples are all waves. Connect speed, frequency and wavelength, and compute wave speed on a string.
Transverse & longitudinal wavesTransverse: particles move perpendicular to the wave (light, string). Longitudinal: particles move along it (sound).
Wave speedv = f·λ (frequency × wavelength). The speed depends on the medium, not on the frequency.
Wave on a stringv = √(T/μ), where T is the tension and μ the mass per unit length. Tighter, lighter strings carry faster waves.
Superposition & beatsOverlapping waves add up (interference/standing waves). Two close frequencies give beats of frequency |f₁ − f₂|.
Wave-speed calculator Interactive
Find the wave speed from frequency and wavelength, and the speed of a wave on a stretched string.
Wave speed, v = f·λ—m/s
On a string, √(T/μ)—m/s
On a guitar, tightening a string (more T) raises the wave speed and hence the pitch.
Numericals practice Interactive
Wave-speed and string problems with steps.
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Solved numericals
Q2. A string of length 1 m fixed at both ends vibrates in its fundamental mode with wave speed 200 m/s. Find the frequency.
Fundamental: λ = 2L = 2 m
f = v/λ = 200/2
f = 100 Hz
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Wave speed | v = f λ | m/s |
| Wave on a string | v = √(T / μ) | m/s |
| Beat frequency | f_beat = |f₁ − f₂| | Hz |
| Frequency–period | f = 1 / T | Hz |
Common mistakes & exam wins
- Wave speed depends on the MEDIUM; changing frequency changes wavelength, not speed.
- On a string, tighter (more T) or lighter (less μ) means a faster wave: v = √(T/μ).
- Beats occur between two nearly-equal frequencies, at f_beat = |f₁ − f₂|.
- For a string fixed at both ends, the fundamental wavelength is twice its length (λ = 2L).
Frequently asked questions
What is the relation between wave speed, frequency and wavelength?
Wave speed = frequency × wavelength, v = fλ. The speed is set by the medium.
What determines the speed of a wave on a string?
The tension and the mass per unit length: v = √(T/μ). Higher tension or lower mass gives a faster wave.
What are beats?
The periodic rise and fall in loudness when two sound waves of nearly equal frequency interfere; the beat frequency is |f₁ − f₂|.