Statements:
1. In a busy street, traffic noise has an intensity of 10⁻² W/m². Find the intensity level in decibels.
2. A mosquito buzzing has an intensity level of 40 dB. Calculate the intensity of this buzzing sound.
3. What is the intensity level of the threshold of hearing and the threshold of pain?
4. The speed of sound waves in water at 25°C is 1480 m/s. If their wavelength is 70 cm, find the frequency of these sound waves.
5. What is the speed of sound at 15°C in air if the speed of sound is 332 m/s at 0°C?
6. Find the range of wavelengths for audible sounds if the minimum frequency is 20 Hz and the maximum frequency is 20 kHz.
7. During a thunderstorm, thunder sound is heard 3 seconds after the lightning flash. Find the distance of the clouds from the ground. (Speed of sound = 340 m/s)
8. A SONAR (Sound Navigation and Ranging) system sends an ultrasound signal towards the sea bed. It is received back after 5.3 s. If the speed of sound in seawater is 1550 m/s, find the depth of the sea bed.
Problem 1: Traffic Noise Intensity Level in Decibels
Given:
- Intensity of sound I=10−2 W/m2
We can calculate the intensity level in decibels (dB) using the formula:
Intensity Level (dB)=10⋅log(I/I0)
where;
- I0=10−12 W/m2 is the threshold of hearing (the quietest sound that the human ear can detect).
Substitute the values:
Intensity Level=10⋅log(10−2/10−12)
=10⋅log(1010) =10⋅10 = 100dB
Answer: The intensity level of the traffic noise is 100 dB.
Problem 2: Intensity of a Mosquito Buzzing (Given Intensity Level)
Given:
- Intensity level of mosquito buzzing L=40 dB
We can calculate the intensity using the formula:
L=10⋅log(I/I0)
Rearranging to solve for :
I/I0=10L/10
I=I0⋅10L/10
Substitute the given values:
- L=40 dB
- I0=10−12 W/m2
I=10−12⋅1040/10
=10−12⋅104
=10−8 W/m2
Answer: The intensity of the mosquito buzzing is 10−8 W/m2
Problem 3: Intensity Levels of Threshold of Hearing and Threshold of Pain
-
Threshold of Hearing: The intensity level of the threshold of hearing is 0 dB, because this is the faintest sound that can be heard.
-
Threshold of Pain: The intensity level of the threshold of pain is about 120 dB, which is the loudest sound the human ear can tolerate before it feels pain.
Answer:
- Threshold of Hearing: 0 dB
- Threshold of Pain: 120 dB
Problem 4: Frequency of Sound Waves in Water
Given:
- Speed of sound in water v=1480 m/s
- Wavelength λ=70 cm=0.7 m
We can use the formula:
v=f⋅λ
Solving for frequency :
f=v/λ
Substitute the given values:
f=1480/0.7=2114.29 Hz
Answer: The frequency of the sound waves is approximately 2114.29 Hz.
Problem 5: Speed of Sound at 15°C
The speed of sound in air increases with temperature. The relationship is given by:
v=v0⋅(1+ΔT/273)
where:
- v0=332 m/s (speed of sound at 0°C)
- ΔT=15−0=15 °C
Substitute the values:
v=332⋅(1+15/273)
v=332⋅(1+0.0549)
v=332⋅1.0549 =349.21 m/s
Answer: The speed of sound at 15°C is approximately 349.21 m/s.
Problem 6: Range of Wavelengths for Audible Sounds
The range of audible sound frequencies is from 20 Hz to 20 kHz. To find the range of wavelengths, we use the formula:
λ=v/f
where:
- v=343 m/s (speed of sound in air at room temperature)
- fmin=20 Hz
- fmax=20 kHz=20000 Hz
For the minimum wavelength:
λmin=343/20000
=0.01715 m
=1.715 cm
For the maximum wavelength:
λmax=343/20
=17.15 m
Answer: The range of wavelengths for audible sounds is from approximately 1.715 cm to 17.15 m.
Problem 7: Distance of Clouds from Ground During Thunderstorm
Given:
- Time delay t=3 s
- Speed of sound v=340 m/s
The distance to the clouds can be found using:
Distance=v⋅t
Substitute the values:
Distance=340⋅3
=1020 m
Answer: The distance of the clouds from the ground is 1020 m.
Problem 8: Depth of Sea Bed Using SONAR
Given:
- Time for signal return t=5.3 s
- Speed of sound in seawater v=1550 m/s
Since the sound travels to the sea bed and back, the actual distance to the sea bed is half of the total distance traveled by the sound:
Distance=v⋅t/2
Substitute the values:
Distance=1550⋅5.3/2
=8215/2
=4107.5 m
Answer: The depth of the sea bed is 4107.5 m.