A string has tension 100 N and linear mass density 0.04 kg/m. What is the wave speed on this string?
A25 m/s
B50 m/s
C2500 m/s
D4 m/s
v = √(T/μ) = √(100/0.04) = √2500 = 50 m/s. Note: doubling tension would multiply speed by √2 (not double it), because speed depends on the square root of tension.
Question 2 Short Answer
A wave travels from a rope with wave speed 40 m/s into a second rope where wave speed is 20 m/s. The wave frequency is 10 Hz. What is the wavelength in each rope?
Think about your answer, then reveal below.
Model answer: In rope 1: λ₁ = v₁/f = 40/10 = 4 m. In rope 2: λ₂ = v₂/f = 20/10 = 2 m. Frequency is unchanged (set by the source); wavelength halves because speed halves.
At a boundary, frequency is conserved and wavelength changes in proportion to speed. This is the key relationship v = fλ applied at the boundary: same f, different v, therefore different λ.
Question 3 Short Answer
A student increases the frequency of a wave on a string by bowing it faster. Does the wave speed on the string change? Does the wavelength change?
Think about your answer, then reveal below.
Model answer: Wave speed does not change — it is determined by the string's tension and linear mass density, which the student hasn't altered. Wavelength does change: since v = fλ and v is fixed, increasing f means λ must decrease (λ = v/f).
This tests the core principle: speed belongs to the medium, frequency belongs to the source. The student controls frequency; the string controls speed. Wavelength is the dependent variable that adjusts to keep v = fλ consistent.