Question

calculating wave speed, frequency and λ 5
name __________________ date ____________ period 1 (2) 3 4
this worksheet is designed to give you some practice using the general wave equation: v=λf. youll be
expected to use this equation correctly on the upcoming chapter test, sound lab and test.

1)
frequency = 5 hz
wavelength = 100 m
speed =

2)
frequency = 20 hz
wavelength = 200 m
speed =

3)
frequency = 27 hz
wavelength = 150 m
speed =

4)
frequency = 27 hz
wavelength =
speed= 46 m/s

5)
frequency =
wavelength = 502 m
speed= 100 m/s

6)
frequency =
wavelength = 326 m
speed = 14 m/s

7)
frequency = 97 hz
wavelength = 1378 m
speed =

8)
frequency = 78 hz
wavelength = 1378 m
speed =

Explanation:

To solve these wave speed, frequency, and wavelength problems, we use the wave equation: \( v = f \times \lambda \), where \( v \) is the speed (in m/s), \( f \) is the frequency (in Hz), and \( \lambda \) is the wavelength (in m). For problems where we need to find frequency or wavelength, we rearrange the formula: \( f = \frac{v}{\lambda} \) or \( \lambda = \frac{v}{f} \).

1) Frequency = 5 Hz, Wavelength = 100 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 5 \, \text{Hz} \) and \( \lambda = 100 \, \text{m} \).
\( v = 5 \times 100 \)

Step 2: Calculate the speed

\( v = 500 \, \text{m/s} \)

2) Frequency = 20 Hz, Wavelength = 200 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 20 \, \text{Hz} \) and \( \lambda = 200 \, \text{m} \).
\( v = 20 \times 200 \)

Step 2: Calculate the speed

\( v = 4000 \, \text{m/s} \)

3) Frequency = 27 Hz, Wavelength = 150 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 27 \, \text{Hz} \) and \( \lambda = 150 \, \text{m} \).
\( v = 27 \times 150 \)

Step 2: Calculate the speed

\( v = 4050 \, \text{m/s} \)

4) Frequency = 27 Hz, Speed = 46 m/s

Step 1: Rearrange the wave equation for wavelength

Use \( \lambda = \frac{v}{f} \). Substitute \( v = 46 \, \text{m/s} \) and \( f = 27 \, \text{Hz} \).
\( \lambda = \frac{46}{27} \)

Step 2: Calculate the wavelength

\( \lambda \approx 1.70 \, \text{m} \) (rounded to two decimal places)

5) Wavelength = 502 m, Speed = 100 m/s

Step 1: Rearrange the wave equation for frequency

Use \( f = \frac{v}{\lambda} \). Substitute \( v = 100 \, \text{m/s} \) and \( \lambda = 502 \, \text{m} \).
\( f = \frac{100}{502} \)

Step 2: Calculate the frequency

\( f \approx 0.20 \, \text{Hz} \) (rounded to two decimal places)

6) Wavelength = 326 m, Speed = 14 m/s

Step 1: Rearrange the wave equation for frequency

Use \( f = \frac{v}{\lambda} \). Substitute \( v = 14 \, \text{m/s} \) and \( \lambda = 326 \, \text{m} \).
\( f = \frac{14}{326} \)

Step 2: Calculate the frequency

\( f \approx 0.04 \, \text{Hz} \) (rounded to two decimal places)

7) Frequency = 97 Hz, Wavelength = 1378 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 97 \, \text{Hz} \) and \( \lambda = 1378 \, \text{m} \).
\( v = 97 \times 1378 \)

Step 2: Calculate the speed

\( v = 133666 \, \text{m/s} \)

8) Frequency = 78 Hz, Wavelength = 137 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 78 \, \text{Hz} \) and \( \lambda = 137 \, \text{m} \).
\( v = 78 \times 137 \)

Step 2: Calculate the speed

\( v = 10686 \, \text{m/s} \)

Final Answers:

1. \( \boldsymbol{500 \, \text{m/s}} \)
2. \( \boldsymbol{4000 \, \text{m/s}} \)
3. \( \boldsymbol{4050 \, \text{m/s}} \)
4. \( \boldsymbol{\approx 1.70 \, \text{m}} \)
5. \( \boldsymbol{\approx 0.20 \, \text{Hz}} \)
6. \( \boldsymbol{\approx 0.04 \, \text{Hz}} \)
7. \( \boldsymbol{133666 \, \text{m/s}} \)
8. \( \boldsymbol{10686 \, \text{m/s}} \)

Answer:

To solve these wave speed, frequency, and wavelength problems, we use the wave equation: \( v = f \times \lambda \), where \( v \) is the speed (in m/s), \( f \) is the frequency (in Hz), and \( \lambda \) is the wavelength (in m). For problems where we need to find frequency or wavelength, we rearrange the formula: \( f = \frac{v}{\lambda} \) or \( \lambda = \frac{v}{f} \).

1) Frequency = 5 Hz, Wavelength = 100 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 5 \, \text{Hz} \) and \( \lambda = 100 \, \text{m} \).
\( v = 5 \times 100 \)

Step 2: Calculate the speed

\( v = 500 \, \text{m/s} \)

2) Frequency = 20 Hz, Wavelength = 200 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 20 \, \text{Hz} \) and \( \lambda = 200 \, \text{m} \).
\( v = 20 \times 200 \)

Step 2: Calculate the speed

\( v = 4000 \, \text{m/s} \)

3) Frequency = 27 Hz, Wavelength = 150 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 27 \, \text{Hz} \) and \( \lambda = 150 \, \text{m} \).
\( v = 27 \times 150 \)

Step 2: Calculate the speed

\( v = 4050 \, \text{m/s} \)

4) Frequency = 27 Hz, Speed = 46 m/s

Step 1: Rearrange the wave equation for wavelength

Use \( \lambda = \frac{v}{f} \). Substitute \( v = 46 \, \text{m/s} \) and \( f = 27 \, \text{Hz} \).
\( \lambda = \frac{46}{27} \)

Step 2: Calculate the wavelength

\( \lambda \approx 1.70 \, \text{m} \) (rounded to two decimal places)

5) Wavelength = 502 m, Speed = 100 m/s

Step 1: Rearrange the wave equation for frequency

Use \( f = \frac{v}{\lambda} \). Substitute \( v = 100 \, \text{m/s} \) and \( \lambda = 502 \, \text{m} \).
\( f = \frac{100}{502} \)

Step 2: Calculate the frequency

\( f \approx 0.20 \, \text{Hz} \) (rounded to two decimal places)

6) Wavelength = 326 m, Speed = 14 m/s

Step 1: Rearrange the wave equation for frequency

Use \( f = \frac{v}{\lambda} \). Substitute \( v = 14 \, \text{m/s} \) and \( \lambda = 326 \, \text{m} \).
\( f = \frac{14}{326} \)

Step 2: Calculate the frequency

\( f \approx 0.04 \, \text{Hz} \) (rounded to two decimal places)

7) Frequency = 97 Hz, Wavelength = 1378 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 97 \, \text{Hz} \) and \( \lambda = 1378 \, \text{m} \).
\( v = 97 \times 1378 \)

Step 2: Calculate the speed

\( v = 133666 \, \text{m/s} \)

8) Frequency = 78 Hz, Wavelength = 137 m

Step 1: Apply the wave equation

Use \( v = f \times \lambda \). Substitute \( f = 78 \, \text{Hz} \) and \( \lambda = 137 \, \text{m} \).
\( v = 78 \times 137 \)

Step 2: Calculate the speed

\( v = 10686 \, \text{m/s} \)

Final Answers:

1. \( \boldsymbol{500 \, \text{m/s}} \)
2. \( \boldsymbol{4000 \, \text{m/s}} \)
3. \( \boldsymbol{4050 \, \text{m/s}} \)
4. \( \boldsymbol{\approx 1.70 \, \text{m}} \)
5. \( \boldsymbol{\approx 0.20 \, \text{Hz}} \)
6. \( \boldsymbol{\approx 0.04 \, \text{Hz}} \)
7. \( \boldsymbol{133666 \, \text{m/s}} \)
8. \( \boldsymbol{10686 \, \text{m/s}} \)