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 one by one.

### Step 1: Analyze the first statement
**Statement:** Wave pulses in strings are transverse waves.
**Analysis:** In a transverse wave, the motion of the particles is perpendicular to the direction of wave propagation. In a string, when a wave pulse travels, the particles of the string move up and down while the wave moves horizontally. This confirms that wave pulses in strings are indeed transverse waves.
**Conclusion:** This statement is **correct**.

### Step 2: Analyze the second statement
**Statement:** Sound waves in air are transverse waves of compression and rarefaction.
**Analysis:** Sound waves in air are longitudinal waves, where the motion of the particles is parallel to the direction of wave propagation. In longitudinal waves, areas of compression and rarefaction occur, but this does not make them transverse waves. Therefore, this statement is incorrect.
**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze the third statement
**Statement:** The speed of sound in air at 20 degrees is twice that at 5 degrees.
**Analysis:** The speed of sound in air is proportional to the square root of the absolute temperature (in Kelvin). At 20 degrees Celsius, the temperature is 293 K, and at 5 degrees Celsius, it is 278 K. The ratio of the speeds is not equal to 2, as the speed of sound does not double with a small change in temperature. Thus, this statement is also incorrect.
**Conclusion:** This statement is **incorrect**.

### Step 4: Analyze the fourth statement
**Statement:** A 60 decibel sound has twice the intensity of a 30 decibel sound.
**Analysis:** The decibel scale is logarithmic. The difference in decibels can be calculated using the formula:
\[ \Delta \beta = 10 \log \left( \frac{I_1}{I_2} \right) \]
If we calculate the difference between 60 dB and 30 dB, we find:
\[ 60 - 30 = 10 \log \left( \frac{I_1}{I_2} \right) \]
This leads to:
\[ 30 = 10 \log \left( \frac{I_1}{I_2} \right) \]
From this, we can deduce that:
\[ \frac{I_1}{I_2} = 10^{3} \]
This means that the intensity of the 60 dB sound is 1000 times greater than that of the 30 dB sound, not twice. Therefore, this statement is incorrect.
**Conclusion:** This statement is **incorrect**.

### Final Conclusion
The incorrect statements are:
- Statement 2: Sound waves in air are transverse waves of compression and rarefaction.
- Statement 3: The speed of sound in air at 20 degrees is twice that at 5 degrees.
- Statement 4: A 60 decibel sound has twice the intensity of a 30 decibel sound.