Question

Sound in water travels at a velocity governed by the relation v = √(B/ρ) where B is the bulk modulus and ρ is the density. For salt water, take B = 2.31 × 109 Pa and ρ = 1063 kg/m3. A whale sends out a high frequency (1 kHz) song to another whale 1.0 km away.

How many wavelengths fit between the whales?

How much time, in seconds, does it take for the sound to travel between the whales, t?

Answer 1

Since speed of sound in medium is given by,

v = sqrt(B/)

for salt water:

given, B = 2.31*10^9 Pa

= 1063 kg/m^3

then, v = speed of sounde in salt water = sqrt[(2.31*10^9)/1063]

v = 1474.14 m/sec.

a.)

Since, v = f*

here, v = speed of sound = 1474.14 m/sec.

f = frequency = 1 kHz = 1000 Hz

then, = wavelength = v/f = 1474.14/1000

= 1.47414 m

Let, 'n' wavelength fits between the whales.

then, n = d/

given, d = distance between whale = 1 km = 1000 m

So, n = 1000/1.47414

n = 678.36

then, number of complete wavelength = 678

b.)

Since, time(t) = distance(d)/speed(v)

using known values:

t = 1000/1474.14

t = 0.678 seconds

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