2.4.2 The speed of the wave
2.2 A certain transverse wave travels at a speed of . The distance between
7 consecutive crests on the wave is 12 cm .
2.2 .1 Define the term wavelength of a wave.
2.2 .2 Determine the wavelength of the wave in metres.
2.2 .3 Calculate the frequency of the wave.

Ask by Cox Erickson. in South Africa

Mar 19,2025

Question

2.4.2 The speed of the wave
2.2 A certain transverse wave travels at a speed of . The distance between
7 consecutive crests on the wave is 12 cm .
2.2 .1 Define the term wavelength of a wave.
2.2 .2 Determine the wavelength of the wave in metres.
2.2 .3 Calculate the frequency of the wave.

Ask by Cox Erickson. in South Africa

Mar 19,2025

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

### 2.2.1 Define the term wavelength of a wave.
**Wavelength** is defined as the distance between two consecutive points that are in phase on a wave, such as the distance between two consecutive crests or troughs. It is usually denoted by the symbol $$ \lambda $$ and is measured in meters (m).

### 2.2.2 Determine the wavelength of the wave in metres.
We are given that the distance between 7 consecutive crests is 12 cm. To find the wavelength, we need to determine the distance between one crest and the next (which is the wavelength).

Since there are 7 crests, there are 6 wavelengths between them. Therefore, we can calculate the wavelength $$ \lambda $$ as follows:

$$
\lambda = \frac{\text{Total distance}}{\text{Number of wavelengths}} = \frac{12 \text{ cm}}{6}
$$

First, we need to convert 12 cm to meters:

$$
12 \text{ cm} = 0.12 \text{ m}
$$

Now we can calculate the wavelength:

$$
\lambda = \frac{0.12 \text{ m}}{6}
$$

Let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.12}{6}$$
- step1: Convert the expressions:
  $$\frac{\frac{3}{25}}{6}$$
- step2: Multiply by the reciprocal:
  $$\frac{3}{25}\times \frac{1}{6}$$
- step3: Reduce the numbers:
  $$\frac{1}{25}\times \frac{1}{2}$$
- step4: Multiply the fractions:
  $$\frac{1}{25\times 2}$$
- step5: Multiply:
  $$\frac{1}{50}$$
The wavelength $$ \lambda $$ of the wave is:

$$
\lambda = 0.02 \text{ m}
$$

### 2.2.3 Calculate the frequency of the wave.
To calculate the frequency $$ f $$ of the wave, we can use the wave speed formula:

$$
v = f \cdot \lambda
$$

Where:
- $$ v $$ is the speed of the wave (given as $$ 0.4 \, \text{m/s} $$),
- $$ f $$ is the frequency (which we need to find),
- $$ \lambda $$ is the wavelength (calculated as $$ 0.02 \, \text{m} $$).

Rearranging the formula to solve for frequency gives us:

$$
f = \frac{v}{\lambda}
$$

Now we can substitute the known values into the equation:

$$
f = \frac{0.4 \, \text{m/s}}{0.02 \, \text{m}}
$$

Let's calculate the frequency.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.4}{0.02}$$
- step1: Convert the expressions:
  $$\frac{\frac{2}{5}}{\frac{1}{50}}$$
- step2: Multiply by the reciprocal:
  $$\frac{2}{5}\times 50$$
- step3: Reduce the numbers:
  $$2\times 10$$
- step4: Multiply the numbers:
  $$20$$
The frequency $$ f $$ of the wave is:

$$
f = 20 \, \text{Hz}
$$

### Summary of Results:
- **Wavelength**: $$ 0.02 \, \text{m} $$
- **Frequency**: $$ 20 \, \text{Hz} $$
**Wavelength**: 0.02 meters **Frequency**: 20 Hz

2.4.2 The speed of the wave
2.2 A certain transverse wave travels at a speed of . The distance between
7 consecutive crests on the wave is 12 cm .
2.2 .1 Define the term wavelength of a wave.
2.2 .2 Determine the wavelength of the wave in metres.
2.2 .3 Calculate the frequency of the wave.

Upstudy AI Solution

Answer

Solution

2.2.1 Define the term wavelength of a wave.

2.2.2 Determine the wavelength of the wave in metres.

2.2.3 Calculate the frequency of the wave.

Summary of Results:

Beyond the Answer

Related Questions

Latest Physics Questions

2.4.2 The speed of the wave 2.2 A certain transverse wave travels at a speed of . The distance between 7 consecutive crests on the wave is 12 cm . 2.2 .1 Define the term wavelength of a wave. 2.2 .2 Determine the wavelength of the wave in metres. 2.2 .3 Calculate the frequency of the wave.

Upstudy AI Solution

Answer

Solution

2.2.1 Define the term wavelength of a wave.

2.2.2 Determine the wavelength of the wave in metres.

2.2.3 Calculate the frequency of the wave.

Summary of Results:

Beyond the Answer

Related Questions

Latest Physics Questions

2.4.2 The speed of the wave
2.2 A certain transverse wave travels at a speed of . The distance between
7 consecutive crests on the wave is 12 cm .
2.2 .1 Define the term wavelength of a wave.
2.2 .2 Determine the wavelength of the wave in metres.
2.2 .3 Calculate the frequency of the wave.