Astationary bagpiper is playing a highland bagpipe, in which one reed produces a continuous sound of frequency 440 hz. the air is still and the speed of sound is 340 m/s. a) what is the wavelength of the sound wave produced by the bagpipe? b)what is the frequency of the sound wave that a bicyclist hears if she is approaching the bagpiper at 10.0 m/s? c)what is the wavelength of the sound wave that a bicyclist hears if she is approaching the bagpiper at 10.0 m/s? d)what is the frequency of the sound wave that a bicyclist hears if she is moving away from the bagpiper at 10.0 m/s? e)what is the wavelength of the sound wave that a bicyclist hears if she is moving away from the bagpiper at 10.0 m/s?

(A) 0.773 m

(B) f' = 452.94 Hz

(C)

(D) f" = 427.058 Hz

(E)

Solution:

As per the question:

Frequency of the sound produced, f = 440 Hz

Speed of the sound in still air, v = 340 m/s

Now,

(A) To calculate the wavelength of the sound wave:

We use the relation:

(B) By using Doppler effect to calculate the frequency of the sound wave:

Velocity of the receiver,

Velocity of the source,

When the receiver is approaching:

f' = 452.94 Hz

(C) To calculate the wavelength of the sound wave:

(D) While moving away, the frequency of the sound wave can be calculated as:

f" = 427.058 Hz

(E) The wavelength can be given by:

C = 771.35 J/kg°C

Explanation:

Here, e consider the conservation of energy equation. The conservation of energy principle states that:

Heat Given by Metal Piece = Heat Absorbed by Water + Heat Absorbed by Container

Since,

Heat Given or Absorbed by a material = m C ΔT

Therefore,

m₁CΔT₁ = m₂CΔT₂ + m₃C₃ΔT₃

where,

m₁ = Mass of Metal Piece = 2.3 kg

C = Specific Heat of Metal = ?

ΔT₁ = Change in temperature of metal piece = 165°C - 18°C = 147°C

m₂ = Mass of Metal Container = 3.8 kg

ΔT₂ = Change in temperature of metal piece = 18°C - 15°C = 3°C

m₃ = Mass of Water = 20 kg

C₃ = Specific Heat of Water = 4200 J/kg°C

ΔT₃ = Change in temperature of water = 18°C - 15°C = 3°C

Therefore,

(2.3 kg)(C)(147°C) = (3.8 kg)(C)(3°C) + (20 kg)(4186 J/kg°C)(3°C)

C[(2.3 kg)(147°C) - (3.8 kg)(3°C)] = 252000 J

C = 252000 J/326.7 kg°C

C = 771.35 J/kg°C