NDA (I) 2025 GAT Q133: The frequency (f), wavelength (λ) and speed (v) of a sound

Q: What is the answer to NDA (I) 2025 GAT Q133?

D. Correct — D, v = lambda.f. For any wave, speed equals frequency times wavelength: v = f.lambda = lambda.f. In one period the wave advances by exactly one wavelength, so distance divided by time equals lambda x f. (Provisional — pending the official UPSC key.)

NDA (I) 2025 General Ability Test · Question 133 of 150

Question text verified against the official NDA question paper.

Provisional answers. UPSC has not yet released the official NDA 2025 answer key (it is published several months after the exam). The answers here are our best-supported answers — derived from careful subject-solving and cross-checked against independent solved papers and primary sources — and will be reconciled to the official key as soon as UPSC publishes it. They are not the official UPSC answer key.

The frequency (f), wavelength (λ) and speed (v) of a sound wave are related as

(a)f = vλ
(b)λ = vf
(c)f = λ / v
(d)v = λf

Answer

Why

Correct — D, v = lambda.f. For any wave, speed equals frequency times wavelength: v = f.lambda = lambda.f. In one period the wave advances by exactly one wavelength, so distance divided by time equals lambda x f.

Why the others are wrong

(a)f = v.lambda — This makes frequency the product of speed and wavelength; correctly f = v/lambda, so it is wrong.
(b)lambda = v.f — Wavelength is speed divided by frequency (lambda = v/f), not their product.
(c)f = lambda / v — This inverts the relation; frequency is v/lambda, not lambda/v.

Concept

A wave's speed (v), frequency (f) and wavelength (lambda) are tied together by v = f.lambda. Frequency is the number of wavelengths passing a point per second; multiplying by the length of each wavelength gives the distance travelled per second, that is, the speed. In a given medium v is fixed, so f and lambda are inversely related.

Rearranging v = f.lambda gives f = v/lambda and lambda = v/f. Each wrong option is a scrambled version of these; only v = lambda.f is physically and dimensionally correct (m/s = (1/s) x m).

Key facts

Wave relation: v = f.lambda (speed = frequency x wavelength).
Equivalently f = v/lambda and lambda = v/f.
In a fixed medium v is constant, so higher frequency means shorter wavelength.
Units check: (1/s) x m = m/s, the unit of speed.

Speed, frequency and wavelength of a wave

v = f x lambda→speed = frequency x wavelength

Rearranged→f = v/lambda and lambda = v/f

Units→(1/s) x m = m/s

Only v = lambda.f is consistent; the other options scramble the relation — option (d).

Study next

Wave parameters: frequency, wavelength, amplitude, periodThe relation v = f.lambda for sound and lightInverse relationship between frequency and wavelengthSpeed of sound in different mediaThe electromagnetic spectrum

Common traps

Rearrange carefully: f = v/lambda, not v.lambda; lambda = v/f, not v.f.
Check units — (1/s) x m gives m/s, confirming v = f.lambda.

Tests the wave equation v = f.lambda, either by picking the correct form or by computing one quantity from the other two.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
A sound wave has a frequency of 500 Hz and a wavelength of 0.66 m. Its speed is
- (a)330 m/s
- (b)758 m/s
- (c)0.0013 m/s
- (d)500 m/s
Answer(a) 330 m/s — v = f.lambda = 500 x 0.66 = 330 m/s.
practice — not a real PYQ
In a given medium, if the frequency of a wave increases, its wavelength
- (a)increases
- (b)decreases
- (c)stays the same
- (d)becomes zero
Answer(b) decreases — since v is fixed, lambda = v/f.