The concept of a sinusoidal wave traveling along a string is included in all secondary education physics books and as a result is being taught in undergraduate lectures around the globe. The didactic approach that follows is advantageous since it provides in a simplified way (through basic mathematical tools) a description of a disturbance that travels through some material or substance. However, in this paper two significant 'paradoxes' that arise when this model is used are presented. Thus, despite its significant value, it should be very carefully used by the instructors in order to prevent students' misconceptions.