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Question 18N.2.SL.TZ0.4b

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Date November 2018 Marks available [Maximum mark: 3] Reference code 18N.2.SL.TZ0.4b
Level SL Paper 2 Time zone TZ0
Command term Determine Question number b Adapted from N/A
b.
[Maximum mark: 3]
18N.2.SL.TZ0.4b

A pipe is open at both ends. A first-harmonic standing wave is set up in the pipe. The diagram shows the variation of displacement of air molecules in the pipe with distance along the pipe at time t = 0. The frequency of the first harmonic is f.

(b)

The speed of sound c for longitudinal waves in air is given by

c = K ρ

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m–3. Determine, in kg m–1 s–2, the value of K for air.

[3]

Markscheme

wavelength = 2 × 1.4 = «2.8 m» ✔

c = «f λ =» 120 × 2.8 «= 340 m s−1» ✔

K = «ρc2 = 1.3 × 3402 =» 1.5 × 105 ✔

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