5.6 Calculations speed of sound

• speed calculations
• Voortgezet speciaal onderwijs
• Leerroute 3

Sound calculations

Learning goals

• Learn to calculate the speed of sound using distance and time
  
• Know the definition of supersonic and Mach

• Learn to calculate the speed of sound using wavelength and frequency
  

Two formulas to calculate the speed of sound

speed=​time​​distance​​

speedofsound=wavelength⋅frequency

speedofsound=wavelength⋅frequency

• Frequency: The number of waves in one second

• Wavelength: the length of one wave
  

• Frequency • wavelength = the distance traveled in one second
  

speed=​time​​distance​​

v=​t​​d​​

• v: speed in m/s
  
• d: distance in m
  
• t: time in s
  

3=​2​​6​​

• v_s: the speed of sound (m/s)
  
• λ: wavelength (m)
• f: frequency (Hz)
  

speedofsound=wavelength⋅frequency

v_s = λ • f

6=2⋅3

Opgave 

 a sound wave were observed to travel a distance of 700 meters in 2 seconds. Calculate its speed.

Given: d= 700 meter , t= 2 s

Asked: v=?

v=d/t.  v= 700/ 2= 350 m/s

Opgave

What is the speed of a sound wave with a frequency of 2 kHz and a wavelength of 35 cm? 

Given: f= 2kHz. = 2000 Hz.    

Asked=?  λ= 35 cm = 0.35 m

v = λ • f = 0.35× 2000= 700 m/s

Calculating the speed of sound  using echoes

A girl stands 102 m away from a wall and claps two wooden blocks together. She hears an echo after 0.6 s.Calculate the speed of sound in air. 

Given: t = 0.6 s.  d=102 + 102 = 204 m.

Asked: v=?

v=d/t  = 204÷ 0.6=340 m/s 

Or  v=d/t. v= 102÷ 0.30 = 340 m/s

Definition supersonic and Mach

Supersonic: faster than speed of sound

Mach 1 = speed of sound in air = 330 m/s

Mach 3 = 330× 3= 990 m/s