Which of the following statements are incorrect?

Options

A. Wave pulses in strings are transverse waves.
B. Sound waves in air are transverse waves of compression and rarefaction.
C. The speed of sound in air at `20^@C` is twice that at `5^@C`.
D. A 60dB sound has twice the intensity of a 30 dB sound.

Explanation

To determine which statements are incorrect, we will analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A**: Waves, pulses, and strings are transverse waves.

- **Explanation**: A transverse wave is defined as a wave in which the direction of particle motion is perpendicular to the direction of wave propagation. In the case of waves on a string, the particles of the string move up and down while the wave travels horizontally along the string. Therefore, this statement is correct.

**Conclusion**: Statement A is correct.

### Step 2: Analyze Statement B
**Statement B**: Sound waves in air are transverse waves of compression and rarefaction.

- **Explanation**: Sound waves are longitudinal waves, meaning the particles of the medium (air) move parallel to the direction of wave propagation. In sound waves, particles compress and rarefy, but they do not move in a perpendicular direction to the wave's motion. Therefore, this statement is incorrect.

**Conclusion**: Statement B is incorrect.

### Step 3: Analyze Statement C
**Statement C**: The speed of sound in air at 20 degrees Celsius is twice that at 5 degrees Celsius.

- **Explanation**: The speed of sound in air is related to temperature by the formula \( V \propto \sqrt{T} \). If we denote the temperatures in Kelvin, we have:
- \( T_1 = 20 + 273 = 293 \, K \)
- \( T_2 = 5 + 273 = 278 \, K \)

The ratio of speeds can be calculated as:
\[ \frac{V_1}{V_2} = \sqrt{\frac{T_1}{T_2}} = \sqrt{\frac{293}{278}} \approx 1.027 \]
This shows that the speed of sound at 20 degrees Celsius is not twice that at 5 degrees Celsius. Therefore, this statement is incorrect.

**Conclusion**: Statement C is incorrect.

### Step 4: Analyze Statement D
**Statement D**: A 60 decibel sound has twice the intensity of a 30 decibel sound.

- **Explanation**: The decibel scale is logarithmic. The formula for sound intensity in decibels is given by:
\[ L = 10 \log \left(\frac{I}{I_0}\right) \]
If we denote the intensity of the 30 dB sound as \( I_1 \) and the intensity of the 60 dB sound as \( I_2 \), we can set up the equations:
\[ 60 = 10 \log \left(\frac{I_2}{I_0}\right) \quad \text{and} \quad 30 = 10 \log \left(\frac{I_1}{I_0}\right) \]
Dividing these two equations gives:
\[ \frac{I_2}{I_1} = 10^{(60-30)/10} = 10^3 = 1000 \]
This means that the intensity of a 60 dB sound is actually 1000 times that of a 30 dB sound, not twice. Therefore, this statement is incorrect.

**Conclusion**: Statement D is incorrect.

### Final Conclusion
The incorrect statements are B, C, and D.

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