A bullet passes past a person at a speed of 220 m/s. Find the fraction

1.	A bullet passes past a person at a speed of 220 m/s. Find the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person. The speed of sound in air = 330 m/s.
Answer» Speed of the source u = 220 m/s. The speed of sound in air = 330 m/s. Let the original frequency =ν. When the bullet is approaching, the source is approaching and the observer is stationary, the apparent frequency ν₁ =Vν/(V-u) =330ν/(330-220) →ν₁ = 330ν/110 =3ν When the bullet has crossed, the source is receding and the observer is stationary. The apparent frequency now, ν₂ = Vν/(V+u) =330ν/(330+220) →ν₂ = 330ν/550 =3ν/5 The change in apparent frequency = ν₁-ν₂ =3ν-3ν/5 = 12ν/5 Hence the fractional change in apparent frequency with respect to initial frequency = (Change in apparent frequency)÷(Initial apparent frequency) =(12ν/5)÷(3ν) =4/5 =0.8

A bullet passes past a person at a speed of 220 m/s. Find the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person. The speed of sound in air = 330 m/s.

Answer»

Speed of the source u = 220 m/s. The speed of sound in air = 330 m/s. Let the original frequency =ν.

When the bullet is approaching, the source is approaching and the observer is stationary, the apparent frequency

ν₁ =Vν/(V-u) =330ν/(330-220)

→ν₁ = 330ν/110 =3ν

When the bullet has crossed, the source is receding and the observer is stationary. The apparent frequency now,

ν₂ = Vν/(V+u) =330ν/(330+220)

→ν₂ = 330ν/550 =3ν/5

The change in apparent frequency = ν₁-ν₂ =3ν-3ν/5 = 12ν/5

Hence the fractional change in apparent frequency with respect to initial frequency = (Change in apparent frequency)÷(Initial apparent frequency)

=(12ν/5)÷(3ν)

=4/5

=0.8

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