Lesson 11 — 1st online lesson

• speed calculations
• Voortgezet speciaal onderwijs
• Leerroute 2

Sound calculations

Learning goals

• Learn to calculate the speed of sound using distance and time
  

• 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

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

Worksheet calculations

Questions 1

a) Write down the two formulas to calculate the speed of sound.

v= d /t       —        vs = λ • f        

b) For each formula, write it out how to transform it for each variable.

v= d  /t          —       d= v • t       —          t= d / v

vs = λ • f        —     λ= vs / f       —          f = vs / λ         

Questions 2

 Explain why doing the wavelength of a wave times the frequency of that wave results in the speed of that wave.

The frequency gives you the amount of waves per second. 

The wavelength gives you the length of each wave in meters.

Multiplying the amount of waves per second times the length of each wave gives you the distance a sound wave travels in one second.

Questions 3

The speed of sound is 343 m/s in air at room temperature.

a) calculate the wavelength of a sound wave with a frequency of 20000 Hz.

λ = vs / f

vs = 343 m/s

f = 20000 Hz

λ = 343 / 20000 = 0.01715 m

b) calculate the frequency of a sound wave with a frequency of 20 Hz.

λ = vs / f

vs = 343 m/s

f = 20 Hz

λ = 343 / 20 = 17.15 m

Questions 4

a) A lighting flash strikes 4459 meters away from someone. 13 seconds later, the thunder is heard. Prove that the speed of sound is 343 m/s. 

v= d /t

d = 4459 m

t = 13 s

v = 4459/13 = 343 m/s

b) If the wavelength of the thunder is 4,9 m, what would its frequency be?

 f = vs / λ

vs = 343 m/s

λ = 4.9 m

 f = 343 /4.9 = 70 Hz

Questions 5

A submarines sonar measures an echo 0.1 second after sending out a sound wave. The speed of sound through water is 1480 m/s. how close is the object the submarine detected?

 v = d / t        —>        d =v • t

v = 1480 m/s

t = 0.1          —>      0.1/2= 0.05.

d = 1480 • 0.05 = 74 m

 (you have to take into account that in echo sound has to travel there and back)

Questions 6

Calculate the frequency of a sound wave traveling through air with a wavelength of 0.6 m.

Note: the speed of sound in air is 343 m/s

f = vs / λ  

vs = 343 m/s

λ = 0.6 m

f = 343 • 0.6 = 205.8 Hz

Learning goals

• Learn to calculate the speed of sound using distance and time
  

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