Question

Choose the incorrect one

• A. When an ultrasonic wave travels from air into water, it bends towards the normal to the air water interface
• B. Any function of the form y(x, t) = f(vt + x) represents a travelling wave
• C. The velocity, wavelength and frequency of wave undergo change when it is reflected from a surface
• D. None of the above

Answer 1

The velocity, wavelength and frequency of wave undergo change when it is reflected from a surface

Answer 2

Let's analyze each statement:

(A) When an ultrasonic wave travels from air into water, it bends towards the normal to the air water interface.
The speed of sound in air is approximately 343 m/s, and the speed of sound in water is approximately 1480 m/s. When a wave travels from a medium where its speed is $v_1$ to a medium where its speed is $v_2$, the refraction is governed by Snell's law: $\frac{\sin i}{\sin r} = \frac{v_1}{v_2}$, where $i$ is the angle of incidence and $r$ is the angle of refraction, both measured from the normal.
In this case, $v_{air} < v_{water}$. So, $\frac{\sin i}{\sin r} = \frac{v_{air}}{v_{water}} < 1$, which means $\sin r > \sin i$. Since $i$ and $r$ are angles between 0 and 90 degrees, this implies $r > i$. If the angle of refraction $r$ is greater than the angle of incidence $i$, the wave bends away from the normal.
The statement says it bends towards the normal, which is incorrect for sound traveling from air to water. This statement is incorrect.

(B) Any function of the form $y(x, t) = f(vt + x)$ represents a travelling wave.
A general form of a travelling wave is $y(x, t) = f(ax \pm bt)$. The argument of the function is of the form $(ax \pm bt)$. The given function $y(x, t) = f(vt + x)$ can be written as $y(x, t) = f(1 \cdot x + v \cdot t)$. This is of the form $f(ax + bt)$ with $a=1$ and $b=v$. This represents a wave travelling in the negative x-direction with a speed of $|b/a| = |v/1| = |v|$. Thus, this function represents a travelling wave. This statement is correct.

(C) The velocity, wavelength and frequency of wave undergo change when it is reflected from a surface.
When a wave is reflected from a surface, it remains in the same medium (or returns to the original medium). The speed of the wave is a property of the medium and does not change upon reflection. The frequency of the wave is determined by the source and does not change upon reflection. Since velocity $v$ and frequency $f$ do not change upon reflection, the wavelength $\lambda = v/f$ also does not change upon reflection.
The statement claims that velocity, wavelength, and frequency undergo change when reflected. This is incorrect. Frequency definitely does not change. Velocity and wavelength also do not change upon reflection from a surface back into the same medium. This statement is incorrect.

We have identified that both statements (A) and (C) are incorrect. Statement (B) is correct. The question asks to choose the incorrect one. Since both (A) and (C) are incorrect, and this is typically a single-choice question format, there might be an error in the question or options. However, if we must choose only one, let's consider if one is more fundamentally incorrect or a more common point of confusion.

Statement (A) is incorrect in the specific case of sound from air to water, but sound can bend towards the normal if it goes from a faster medium to a slower medium.
Statement (C) claims that velocity, wavelength, and frequency all change upon reflection. This is a very strong claim, and it is incorrect because frequency never changes upon reflection, and velocity and wavelength also do not change upon reflection into the same medium.

Given that the question is likely single-choice, and both (A) and (C) are incorrect, there is an issue with the question. However, if forced to choose the most incorrect statement or the one that is incorrect in the most general sense among the incorrect ones, statement (C) is a broad claim about reflection that is false regarding all three mentioned properties. Statement (A) is incorrect for a specific case of refraction.