Answer :
Sure, here is the detailed step-by-step solution to your question.
### 4. Direction of Oscillations
#### (i) Transverse Wave
A transverse wave is characterized by the direction in which the wave oscillates. In a transverse wave, the oscillations of the medium particles are perpendicular to the direction of wave propagation. This means if the wave is moving in a horizontal direction, the particles of the medium move up and down or side to side along the vertical direction.
#### (ii) Longitudinal Wave
In a longitudinal wave, the oscillations of the medium particles are parallel to the direction of wave propagation. This means if the wave is moving in a horizontal direction, the particles of the medium move back and forth along the horizontal direction as well.
### 5. Time Calculation for a Sound Wave to Travel 1.6 km
Given:
- Frequency of the sound wave, [tex]\( f = \text{2000 Hz (2 kHz)} \)[/tex]
- Wavelength of the sound wave, [tex]\( \lambda = \text{0.4 meters (40 cm)} \)[/tex]
- Distance to travel, [tex]\( d = \text{1600 meters (1.6 km)} \)[/tex]
Step-by-Step Solution:
1. Calculating the Speed of Sound:
The speed of sound [tex]\( v \)[/tex] can be determined using the formula:
[tex]\[ v = f \times \lambda \][/tex]
Given data:
- Frequency, [tex]\( f = 2000 \)[/tex] Hz
- Wavelength, [tex]\( \lambda = 0.4 \)[/tex] meters
Plugging in the values:
[tex]\[ v = 2000 \, \text{Hz} \times 0.4 \, \text{m} \][/tex]
[tex]\[ v = 800 \, \text{m/s} \][/tex]
So, the speed of sound is [tex]\( 800 \)[/tex] meters per second.
2. Calculating the Time to Travel 1.6 km:
The time [tex]\( t \)[/tex] it takes for the sound to travel a given distance can be found using the formula:
[tex]\[ t = \frac{d}{v} \][/tex]
Given data:
- Distance, [tex]\( d = 1600 \)[/tex] meters
- Speed of sound, [tex]\( v = 800 \)[/tex] meters per second
Plugging in the values:
[tex]\[ t = \frac{1600 \, \text{m}}{800 \, \text{m/s}} \][/tex]
[tex]\[ t = 2 \, \text{seconds} \][/tex]
So, it will take 2 seconds for the sound wave to travel 1.6 km.
### Summary of Answers:
1. Direction of oscillations:
- (i) Transverse wave: Perpendicular to the direction of wave propagation.
- (ii) Longitudinal wave: Parallel to the direction of wave propagation.
2. Time for a sound wave with frequency 2 kHz and wavelength 40 cm to travel 1.6 km: 2 seconds.
### 4. Direction of Oscillations
#### (i) Transverse Wave
A transverse wave is characterized by the direction in which the wave oscillates. In a transverse wave, the oscillations of the medium particles are perpendicular to the direction of wave propagation. This means if the wave is moving in a horizontal direction, the particles of the medium move up and down or side to side along the vertical direction.
#### (ii) Longitudinal Wave
In a longitudinal wave, the oscillations of the medium particles are parallel to the direction of wave propagation. This means if the wave is moving in a horizontal direction, the particles of the medium move back and forth along the horizontal direction as well.
### 5. Time Calculation for a Sound Wave to Travel 1.6 km
Given:
- Frequency of the sound wave, [tex]\( f = \text{2000 Hz (2 kHz)} \)[/tex]
- Wavelength of the sound wave, [tex]\( \lambda = \text{0.4 meters (40 cm)} \)[/tex]
- Distance to travel, [tex]\( d = \text{1600 meters (1.6 km)} \)[/tex]
Step-by-Step Solution:
1. Calculating the Speed of Sound:
The speed of sound [tex]\( v \)[/tex] can be determined using the formula:
[tex]\[ v = f \times \lambda \][/tex]
Given data:
- Frequency, [tex]\( f = 2000 \)[/tex] Hz
- Wavelength, [tex]\( \lambda = 0.4 \)[/tex] meters
Plugging in the values:
[tex]\[ v = 2000 \, \text{Hz} \times 0.4 \, \text{m} \][/tex]
[tex]\[ v = 800 \, \text{m/s} \][/tex]
So, the speed of sound is [tex]\( 800 \)[/tex] meters per second.
2. Calculating the Time to Travel 1.6 km:
The time [tex]\( t \)[/tex] it takes for the sound to travel a given distance can be found using the formula:
[tex]\[ t = \frac{d}{v} \][/tex]
Given data:
- Distance, [tex]\( d = 1600 \)[/tex] meters
- Speed of sound, [tex]\( v = 800 \)[/tex] meters per second
Plugging in the values:
[tex]\[ t = \frac{1600 \, \text{m}}{800 \, \text{m/s}} \][/tex]
[tex]\[ t = 2 \, \text{seconds} \][/tex]
So, it will take 2 seconds for the sound wave to travel 1.6 km.
### Summary of Answers:
1. Direction of oscillations:
- (i) Transverse wave: Perpendicular to the direction of wave propagation.
- (ii) Longitudinal wave: Parallel to the direction of wave propagation.
2. Time for a sound wave with frequency 2 kHz and wavelength 40 cm to travel 1.6 km: 2 seconds.
