Calculate with sound

• physics
• Middelbare school
• havo, vwo
• Leerjaar 2

Calculate with sound

Formulas:

f = 1/T

T = period in s

f = frequency in Hz

T = 1/f

f = frequency in Hz

T = period in s

Converting

ms to s (: 1000)

kHz to Hz (x 1000)

Hz to kHz (:1000)

s = v x t

v = speed in m/s

t = time in s

s = distance in m

1. Calculate

time/div = 0.2 ms/div

Calculate the frequency

2. Tones

a. Which picture shows the highest tone?

b. Which picture shows the lowest tone?

c. Which picture shows the loudest tone?

3. 

You see a musical box. When you rotate the handle, you hear a melody.

a. Which bars produce the lowest tones, the short or the long ones?

b. Which bars produce the highest tones?

4. Oscilloscope

a. Read the period of one vibration (click on picture to enlarge).

b. Calculate the frequency.

5. Piano

A piano string produces vibrations with a period of 2.5 ms.

a. Convert the period into seconds.

b. What is the frequency f?

c. Convert the frequency to kHz.

6. Air-raid siren

This is an old fashioned air-raid siren. Air is driven via a tube onto the rotating disc. The air is forced through 30 holes in the disc. This creates a vibration which produces a loud sound. The disc rotates 5 times per second.

6.

a. How many times per second does a hole appear below the opening of the air pipe?

b. Explain why you hear a tone of 150 Hz

6

The siren starts slowly and the gradually becomes higher. At full speed the tone is 1.8 kHz.

c. Calculate the periode of this frequency.

d. How many times per second does the disc rotate now?

7

At a firework display, Phil sees a rocket explode 124 m above his head. The sound of speed is 340 m/s. 

Calculate how much later Phil hears the bang.

1.

Given: 0.2 ms/div

1 vibration is 5 blocks (div)

Asked: f

Solution: f = 1/T

T = 5 x 0.2 ms = 1 ms

1 ms :1000 = 0.001 s

f = 1 / 0.001 s = 1000 Hz

2.

a.  C- most vibrations in 0.01 s

b. B- least amount of vibrations in 0.01 s

c. A - biggest displacement (in y-direction) 

3.

a. The longest ones

b. The shortest ones

4. 

a. One vibration lasts 1.82 ms (easiest to see from 6 to 7.82 ms)

b. Given: T = 1.82 ms = 1.82:1000 = 0.00182 s

Asked: f

Solution: f = 1/T

f = 1 / 0.00182 = 549,5 Hz

5.

a. T= 2.5 ms = 2.5 : 1000 = 0.0025 s

b. Given: T = 0.0025 s

Asked: f

Solution: f = 1/T

f = 1/ 0.0025 = 400 Hz

c. f = 400 Hz = 400 : 1000 = 0.4 kHz

6

a. The disc turns 5 times per second. 5 Times the 30 holes in the disc are 150 holes. 150 Holes pass the air pipe per second.

b. Every time the air is blown into the hole and then interrupted by the solid part in between the holes, creates a sound. This happens 150 times per second = at a frequency of 150 Hertz.

6

c. f = 1.8 kHz = 1.8 kHz x 1000 = 1800 Hz

d. Given f = 1800 Hz

30 holes in the disc

Asked: amount of rotations per second

Solution: 1800 holes pas per second

1800 : 30 holes per rotation = 60 rotations per second

7

Given: s (distance) = 124 m

v (speed) = 340 m/s

Asked: t (time)

Solution: s = v x t

t = s / v = 124 m / 340 m/s = 0.36 seconds

Phil hears the blast after 0.36 seconds.